Locally Recoverable Codes Over Zp s
Locally recoverable codes (LRCs) play a vital role in distributed storage systems where the failure or unavailability of storage devices is a common occurrence. The purpose of LRCs is to facilitate the repair processes required to recover lost or damaged data in such systems. A code C will be said...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on communications 2024-05, Vol.72 (5), p.2503-2518 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 2518 |
|---|---|
| container_issue | 5 |
| container_start_page | 2503 |
| container_title | IEEE transactions on communications |
| container_volume | 72 |
| creator | Kourani, Nasim Abdi Khodaiemehr, Hassan Nikmehr, Mohammad Javad |
| description | Locally recoverable codes (LRCs) play a vital role in distributed storage systems where the failure or unavailability of storage devices is a common occurrence. The purpose of LRCs is to facilitate the repair processes required to recover lost or damaged data in such systems. A code C will be said \left ({r,\delta }\right) -LRC if for each i , the i th component of codewords have locality (r, \delta) , that is, there exists a punctured subcode of C with support containing i , whose length is at most r + \delta - 1 , and whose minimum distance is at least \delta . An (r, \delta) -LRC with locality (r, \delta) allows for the local recovery of any \delta -1 nodes by accessing information from r other nodes. In this paper, we present new constructions of \left ({r,\delta }\right) -LRCs, with 2\leq \delta \leq \frac {p-1}{t} over \mathbb {Z}_{p^{s}} , where t divides p-1 and t\neq p-1 . Initially, we provide generator matrices for \left ({r,2}\right) -LRCs, among which one instance is considered as Singleton-Type Bound (STB)-optimal, a notio |
| doi_str_mv | 10.1109/TCOMM.2024.3351760 |
| format | Article |
| fullrecord | <record><control><sourceid>ieee_RIE</sourceid><recordid>TN_cdi_ieee_primary_10385182</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>10385182</ieee_id><sourcerecordid>10385182</sourcerecordid><originalsourceid>FETCH-LOGICAL-i106t-1d0bbb08a3d0ea89f97dffdf6868a4d488a057653a7c07227cca2cc820356ba13</originalsourceid><addsrcrecordid>eNotzM1Kw0AUQOFZKFhrX0BcDLhOvDM3M3OzlKBWSAlIu3FT7vxBJJKSEaFvr6Crw7c5QtwqqJWC9mHfDbtdrUE3NaJRzsKFWAG0UFnn6Epcl_IBAA0grsR9PweeprN8S2H-Tgv7KclujqnI4Zfy_STLjbjMPJW0-e9aHJ6f9t226oeX1-6xr0YF9qtSEbz3QIwRElObWxdzjtmSJW5iQ8RgnDXILoDT2oXAOgTSgMZ6VrgWd3_fMaV0PC3jJy_nowIko0jjD1jnPAo</addsrcrecordid><sourcetype>Publisher</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Locally Recoverable Codes Over Zp s</title><source>IEEE Electronic Library (IEL)</source><creator>Kourani, Nasim Abdi ; Khodaiemehr, Hassan ; Nikmehr, Mohammad Javad</creator><creatorcontrib>Kourani, Nasim Abdi ; Khodaiemehr, Hassan ; Nikmehr, Mohammad Javad</creatorcontrib><description><![CDATA[Locally recoverable codes (LRCs) play a vital role in distributed storage systems where the failure or unavailability of storage devices is a common occurrence. The purpose of LRCs is to facilitate the repair processes required to recover lost or damaged data in such systems. A code <inline-formula> <tex-math notation="LaTeX">C </tex-math></inline-formula> will be said <inline-formula> <tex-math notation="LaTeX">\left ({r,\delta }\right) </tex-math></inline-formula>-LRC if for each <inline-formula> <tex-math notation="LaTeX">i </tex-math></inline-formula>, the <inline-formula> <tex-math notation="LaTeX">i </tex-math></inline-formula>th component of codewords have locality <inline-formula> <tex-math notation="LaTeX">(r, \delta) </tex-math></inline-formula>, that is, there exists a punctured subcode of <inline-formula> <tex-math notation="LaTeX">C </tex-math></inline-formula> with support containing <inline-formula> <tex-math notation="LaTeX">i </tex-math></inline-formula>, whose length is at most <inline-formula> <tex-math notation="LaTeX">r + \delta - 1 </tex-math></inline-formula>, and whose minimum distance is at least <inline-formula> <tex-math notation="LaTeX">\delta </tex-math></inline-formula>. An <inline-formula> <tex-math notation="LaTeX">(r, \delta) </tex-math></inline-formula>-LRC with locality <inline-formula> <tex-math notation="LaTeX">(r, \delta) </tex-math></inline-formula> allows for the local recovery of any <inline-formula> <tex-math notation="LaTeX">\delta -1 </tex-math></inline-formula> nodes by accessing information from <inline-formula> <tex-math notation="LaTeX">r </tex-math></inline-formula> other nodes. In this paper, we present new constructions of <inline-formula> <tex-math notation="LaTeX">\left ({r,\delta }\right) </tex-math></inline-formula>-LRCs, with <inline-formula> <tex-math notation="LaTeX">2\leq \delta \leq \frac {p-1}{t} </tex-math></inline-formula> over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">t </tex-math></inline-formula> divides <inline-formula> <tex-math notation="LaTeX">p-1 </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">t\neq p-1 </tex-math></inline-formula>. Initially, we provide generator matrices for <inline-formula> <tex-math notation="LaTeX">\left ({r,2}\right) </tex-math></inline-formula>-LRCs, among which one instance is considered as Singleton-Type Bound (STB)-optimal, a notion introduced in this paper. Also, we present a method for recovering an erased symbol in a codeword of our <inline-formula> <tex-math notation="LaTeX">\left ({r,2}\right) </tex-math></inline-formula>-LRC. For this aim, we use the polynomial interpolation over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula> proposed by Gopalan. Next, we present the parity-check matrices for another family of <inline-formula> <tex-math notation="LaTeX">\left ({r,\delta }\right) </tex-math></inline-formula>-LRCs over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula>, and construct two instances of STB-optimal <inline-formula> <tex-math notation="LaTeX">\left ({r,\delta }\right) </tex-math></inline-formula>-LRCs. To the best of our knowledge, this paper presents the first study on ring-based LRCs. The proposed LRCs over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula> exhibit certain design restrictions compared to LRCs over <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{p^{s}} </tex-math></inline-formula>. However, we provide two advantages for LRCs over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula>. First, we analyze Boolean circuits for arithmetic operations and demonstrate that the complexity of implementing multiplication in <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula>, the operation with the highest cost in our algorithms, is considerably lower than in <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{p^{s}} </tex-math></inline-formula>. This highlights the superior performance of our LRCs in terms of implementation speed and cost-efficiency compared to their counterparts. Next, we offer an example illustrating that the Gray image of particular <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s+1}} </tex-math></inline-formula>-LRCs of length <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> results in LRCs of length <inline-formula> <tex-math notation="LaTeX">np^{s} </tex-math></inline-formula> over <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{p} </tex-math></inline-formula>, which may not necessarily be linear. This introduces a novel class of LRCs, prompting further exploration of the connections between existing nonlinear LRCs in finite fields and linear ring-based LRCs.]]></description><identifier>ISSN: 0090-6778</identifier><identifier>DOI: 10.1109/TCOMM.2024.3351760</identifier><identifier>CODEN: IECMBT</identifier><language>eng</language><publisher>IEEE</publisher><subject>Codes ; distributed storage system ; erasure code ; Generators ; Hamming distances ; Interpolation ; Linear codes ; Locally recoverable code ; Maintenance engineering ; Symbols</subject><ispartof>IEEE transactions on communications, 2024-05, Vol.72 (5), p.2503-2518</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000-0002-0489-8546 ; 0009-0003-3919-5538 ; 0000-0001-6912-3955</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/10385182$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/10385182$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Kourani, Nasim Abdi</creatorcontrib><creatorcontrib>Khodaiemehr, Hassan</creatorcontrib><creatorcontrib>Nikmehr, Mohammad Javad</creatorcontrib><title>Locally Recoverable Codes Over Zp s</title><title>IEEE transactions on communications</title><addtitle>TCOMM</addtitle><description><![CDATA[Locally recoverable codes (LRCs) play a vital role in distributed storage systems where the failure or unavailability of storage devices is a common occurrence. The purpose of LRCs is to facilitate the repair processes required to recover lost or damaged data in such systems. A code <inline-formula> <tex-math notation="LaTeX">C </tex-math></inline-formula> will be said <inline-formula> <tex-math notation="LaTeX">\left ({r,\delta }\right) </tex-math></inline-formula>-LRC if for each <inline-formula> <tex-math notation="LaTeX">i </tex-math></inline-formula>, the <inline-formula> <tex-math notation="LaTeX">i </tex-math></inline-formula>th component of codewords have locality <inline-formula> <tex-math notation="LaTeX">(r, \delta) </tex-math></inline-formula>, that is, there exists a punctured subcode of <inline-formula> <tex-math notation="LaTeX">C </tex-math></inline-formula> with support containing <inline-formula> <tex-math notation="LaTeX">i </tex-math></inline-formula>, whose length is at most <inline-formula> <tex-math notation="LaTeX">r + \delta - 1 </tex-math></inline-formula>, and whose minimum distance is at least <inline-formula> <tex-math notation="LaTeX">\delta </tex-math></inline-formula>. An <inline-formula> <tex-math notation="LaTeX">(r, \delta) </tex-math></inline-formula>-LRC with locality <inline-formula> <tex-math notation="LaTeX">(r, \delta) </tex-math></inline-formula> allows for the local recovery of any <inline-formula> <tex-math notation="LaTeX">\delta -1 </tex-math></inline-formula> nodes by accessing information from <inline-formula> <tex-math notation="LaTeX">r </tex-math></inline-formula> other nodes. In this paper, we present new constructions of <inline-formula> <tex-math notation="LaTeX">\left ({r,\delta }\right) </tex-math></inline-formula>-LRCs, with <inline-formula> <tex-math notation="LaTeX">2\leq \delta \leq \frac {p-1}{t} </tex-math></inline-formula> over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">t </tex-math></inline-formula> divides <inline-formula> <tex-math notation="LaTeX">p-1 </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">t\neq p-1 </tex-math></inline-formula>. Initially, we provide generator matrices for <inline-formula> <tex-math notation="LaTeX">\left ({r,2}\right) </tex-math></inline-formula>-LRCs, among which one instance is considered as Singleton-Type Bound (STB)-optimal, a notion introduced in this paper. Also, we present a method for recovering an erased symbol in a codeword of our <inline-formula> <tex-math notation="LaTeX">\left ({r,2}\right) </tex-math></inline-formula>-LRC. For this aim, we use the polynomial interpolation over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula> proposed by Gopalan. Next, we present the parity-check matrices for another family of <inline-formula> <tex-math notation="LaTeX">\left ({r,\delta }\right) </tex-math></inline-formula>-LRCs over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula>, and construct two instances of STB-optimal <inline-formula> <tex-math notation="LaTeX">\left ({r,\delta }\right) </tex-math></inline-formula>-LRCs. To the best of our knowledge, this paper presents the first study on ring-based LRCs. The proposed LRCs over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula> exhibit certain design restrictions compared to LRCs over <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{p^{s}} </tex-math></inline-formula>. However, we provide two advantages for LRCs over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula>. First, we analyze Boolean circuits for arithmetic operations and demonstrate that the complexity of implementing multiplication in <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula>, the operation with the highest cost in our algorithms, is considerably lower than in <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{p^{s}} </tex-math></inline-formula>. This highlights the superior performance of our LRCs in terms of implementation speed and cost-efficiency compared to their counterparts. Next, we offer an example illustrating that the Gray image of particular <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s+1}} </tex-math></inline-formula>-LRCs of length <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> results in LRCs of length <inline-formula> <tex-math notation="LaTeX">np^{s} </tex-math></inline-formula> over <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{p} </tex-math></inline-formula>, which may not necessarily be linear. This introduces a novel class of LRCs, prompting further exploration of the connections between existing nonlinear LRCs in finite fields and linear ring-based LRCs.]]></description><subject>Codes</subject><subject>distributed storage system</subject><subject>erasure code</subject><subject>Generators</subject><subject>Hamming distances</subject><subject>Interpolation</subject><subject>Linear codes</subject><subject>Locally recoverable code</subject><subject>Maintenance engineering</subject><subject>Symbols</subject><issn>0090-6778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNotzM1Kw0AUQOFZKFhrX0BcDLhOvDM3M3OzlKBWSAlIu3FT7vxBJJKSEaFvr6Crw7c5QtwqqJWC9mHfDbtdrUE3NaJRzsKFWAG0UFnn6Epcl_IBAA0grsR9PweeprN8S2H-Tgv7KclujqnI4Zfy_STLjbjMPJW0-e9aHJ6f9t226oeX1-6xr0YF9qtSEbz3QIwRElObWxdzjtmSJW5iQ8RgnDXILoDT2oXAOgTSgMZ6VrgWd3_fMaV0PC3jJy_nowIko0jjD1jnPAo</recordid><startdate>202405</startdate><enddate>202405</enddate><creator>Kourani, Nasim Abdi</creator><creator>Khodaiemehr, Hassan</creator><creator>Nikmehr, Mohammad Javad</creator><general>IEEE</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><orcidid>https://orcid.org/0000-0002-0489-8546</orcidid><orcidid>https://orcid.org/0009-0003-3919-5538</orcidid><orcidid>https://orcid.org/0000-0001-6912-3955</orcidid></search><sort><creationdate>202405</creationdate><title>Locally Recoverable Codes Over Zp s</title><author>Kourani, Nasim Abdi ; Khodaiemehr, Hassan ; Nikmehr, Mohammad Javad</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-i106t-1d0bbb08a3d0ea89f97dffdf6868a4d488a057653a7c07227cca2cc820356ba13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Codes</topic><topic>distributed storage system</topic><topic>erasure code</topic><topic>Generators</topic><topic>Hamming distances</topic><topic>Interpolation</topic><topic>Linear codes</topic><topic>Locally recoverable code</topic><topic>Maintenance engineering</topic><topic>Symbols</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kourani, Nasim Abdi</creatorcontrib><creatorcontrib>Khodaiemehr, Hassan</creatorcontrib><creatorcontrib>Nikmehr, Mohammad Javad</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><jtitle>IEEE transactions on communications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kourani, Nasim Abdi</au><au>Khodaiemehr, Hassan</au><au>Nikmehr, Mohammad Javad</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Locally Recoverable Codes Over Zp s</atitle><jtitle>IEEE transactions on communications</jtitle><stitle>TCOMM</stitle><date>2024-05</date><risdate>2024</risdate><volume>72</volume><issue>5</issue><spage>2503</spage><epage>2518</epage><pages>2503-2518</pages><issn>0090-6778</issn><coden>IECMBT</coden><abstract><![CDATA[Locally recoverable codes (LRCs) play a vital role in distributed storage systems where the failure or unavailability of storage devices is a common occurrence. The purpose of LRCs is to facilitate the repair processes required to recover lost or damaged data in such systems. A code <inline-formula> <tex-math notation="LaTeX">C </tex-math></inline-formula> will be said <inline-formula> <tex-math notation="LaTeX">\left ({r,\delta }\right) </tex-math></inline-formula>-LRC if for each <inline-formula> <tex-math notation="LaTeX">i </tex-math></inline-formula>, the <inline-formula> <tex-math notation="LaTeX">i </tex-math></inline-formula>th component of codewords have locality <inline-formula> <tex-math notation="LaTeX">(r, \delta) </tex-math></inline-formula>, that is, there exists a punctured subcode of <inline-formula> <tex-math notation="LaTeX">C </tex-math></inline-formula> with support containing <inline-formula> <tex-math notation="LaTeX">i </tex-math></inline-formula>, whose length is at most <inline-formula> <tex-math notation="LaTeX">r + \delta - 1 </tex-math></inline-formula>, and whose minimum distance is at least <inline-formula> <tex-math notation="LaTeX">\delta </tex-math></inline-formula>. An <inline-formula> <tex-math notation="LaTeX">(r, \delta) </tex-math></inline-formula>-LRC with locality <inline-formula> <tex-math notation="LaTeX">(r, \delta) </tex-math></inline-formula> allows for the local recovery of any <inline-formula> <tex-math notation="LaTeX">\delta -1 </tex-math></inline-formula> nodes by accessing information from <inline-formula> <tex-math notation="LaTeX">r </tex-math></inline-formula> other nodes. In this paper, we present new constructions of <inline-formula> <tex-math notation="LaTeX">\left ({r,\delta }\right) </tex-math></inline-formula>-LRCs, with <inline-formula> <tex-math notation="LaTeX">2\leq \delta \leq \frac {p-1}{t} </tex-math></inline-formula> over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">t </tex-math></inline-formula> divides <inline-formula> <tex-math notation="LaTeX">p-1 </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">t\neq p-1 </tex-math></inline-formula>. Initially, we provide generator matrices for <inline-formula> <tex-math notation="LaTeX">\left ({r,2}\right) </tex-math></inline-formula>-LRCs, among which one instance is considered as Singleton-Type Bound (STB)-optimal, a notion introduced in this paper. Also, we present a method for recovering an erased symbol in a codeword of our <inline-formula> <tex-math notation="LaTeX">\left ({r,2}\right) </tex-math></inline-formula>-LRC. For this aim, we use the polynomial interpolation over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula> proposed by Gopalan. Next, we present the parity-check matrices for another family of <inline-formula> <tex-math notation="LaTeX">\left ({r,\delta }\right) </tex-math></inline-formula>-LRCs over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula>, and construct two instances of STB-optimal <inline-formula> <tex-math notation="LaTeX">\left ({r,\delta }\right) </tex-math></inline-formula>-LRCs. To the best of our knowledge, this paper presents the first study on ring-based LRCs. The proposed LRCs over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula> exhibit certain design restrictions compared to LRCs over <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{p^{s}} </tex-math></inline-formula>. However, we provide two advantages for LRCs over <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula>. First, we analyze Boolean circuits for arithmetic operations and demonstrate that the complexity of implementing multiplication in <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s}} </tex-math></inline-formula>, the operation with the highest cost in our algorithms, is considerably lower than in <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{p^{s}} </tex-math></inline-formula>. This highlights the superior performance of our LRCs in terms of implementation speed and cost-efficiency compared to their counterparts. Next, we offer an example illustrating that the Gray image of particular <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{p^{s+1}} </tex-math></inline-formula>-LRCs of length <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> results in LRCs of length <inline-formula> <tex-math notation="LaTeX">np^{s} </tex-math></inline-formula> over <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{p} </tex-math></inline-formula>, which may not necessarily be linear. This introduces a novel class of LRCs, prompting further exploration of the connections between existing nonlinear LRCs in finite fields and linear ring-based LRCs.]]></abstract><pub>IEEE</pub><doi>10.1109/TCOMM.2024.3351760</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0002-0489-8546</orcidid><orcidid>https://orcid.org/0009-0003-3919-5538</orcidid><orcidid>https://orcid.org/0000-0001-6912-3955</orcidid></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 0090-6778 |
| ispartof | IEEE transactions on communications, 2024-05, Vol.72 (5), p.2503-2518 |
| issn | 0090-6778 |
| language | eng |
| recordid | cdi_ieee_primary_10385182 |
| source | IEEE Electronic Library (IEL) |
| subjects | Codes distributed storage system erasure code Generators Hamming distances Interpolation Linear codes Locally recoverable code Maintenance engineering Symbols |
| title | Locally Recoverable Codes Over Zp s |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-03T16%3A20%3A37IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-ieee_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Locally%20Recoverable%20Codes%20Over%20Zp%20s&rft.jtitle=IEEE%20transactions%20on%20communications&rft.au=Kourani,%20Nasim%20Abdi&rft.date=2024-05&rft.volume=72&rft.issue=5&rft.spage=2503&rft.epage=2518&rft.pages=2503-2518&rft.issn=0090-6778&rft.coden=IECMBT&rft_id=info:doi/10.1109/TCOMM.2024.3351760&rft_dat=%3Cieee_RIE%3E10385182%3C/ieee_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_ieee_id=10385182&rfr_iscdi=true |