Minimal Linear Codes From Characteristic Functions
Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of \mathbb {F}_{q} to construct minimal linear codes. By properties of characteristic functions, we can obtain more minimal binary...
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| Veröffentlicht in: | IEEE transactions on information theory 2020-09, Vol.66 (9), p.5404-5413 |
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| creator | Mesnager, Sihem Qi, Yanfeng Ru, Hongming Tang, Chunming |
| description | Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of \mathbb {F}_{q} to construct minimal linear codes. By properties of characteristic functions, we can obtain more minimal binary linear codes from known minimal binary linear codes, which generalizes results of Ding et al. [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018]. By characteristic functions corresponding to some subspaces of \mathbb {F}_{q} , we obtain many minimal linear codes, which generalizes results of [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018] and [IEEE Trans. Inf. Theory, vol. 65, no. 11, pp. 7067-7078, 2019]. Finally, we use characteristic functions to present a characterization of minimal linear codes from the defining set method and present a class of minimal linear codes. |
| doi_str_mv | 10.1109/TIT.2020.2978387 |
| format | Article |
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This paper uses characteristic functions of some subsets of <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{q} </tex-math></inline-formula> to construct minimal linear codes. By properties of characteristic functions, we can obtain more minimal binary linear codes from known minimal binary linear codes, which generalizes results of Ding et al. [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018]. By characteristic functions corresponding to some subspaces of <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{q} </tex-math></inline-formula>, we obtain many minimal linear codes, which generalizes results of [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018] and [IEEE Trans. Inf. Theory, vol. 65, no. 11, pp. 7067-7078, 2019]. Finally, we use characteristic functions to present a characterization of minimal linear codes from the defining set method and present a class of minimal linear codes.]]></description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2020.2978387</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Binary codes ; Binary system ; Boolean functions ; characteristic function ; Characteristic functions ; Codes ; Cryptography ; Electronic mail ; Frequency modulation ; Hamming weight ; Linear codes ; Mathematics ; Minimal linear code ; subspace ; Subspaces ; weight distribution</subject><ispartof>IEEE transactions on information theory, 2020-09, Vol.66 (9), p.5404-5413</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2020</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c325t-d113bf71b335116b80d175ecdf40459fcde319e95299bc7e0a7b75794af236d3</citedby><cites>FETCH-LOGICAL-c325t-d113bf71b335116b80d175ecdf40459fcde319e95299bc7e0a7b75794af236d3</cites><orcidid>0000-0003-1381-5471 ; 0000-0001-9599-851X ; 0000-0003-4008-2031</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/9025180$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>230,314,776,780,792,881,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/9025180$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttps://telecom-paris.hal.science/hal-03973281$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Mesnager, Sihem</creatorcontrib><creatorcontrib>Qi, Yanfeng</creatorcontrib><creatorcontrib>Ru, Hongming</creatorcontrib><creatorcontrib>Tang, Chunming</creatorcontrib><title>Minimal Linear Codes From Characteristic Functions</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description><![CDATA[Minimal linear codes have interesting applications in secret sharing schemes and secure two-party computation. This paper uses characteristic functions of some subsets of <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{q} </tex-math></inline-formula> to construct minimal linear codes. By properties of characteristic functions, we can obtain more minimal binary linear codes from known minimal binary linear codes, which generalizes results of Ding et al. [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018]. By characteristic functions corresponding to some subspaces of <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{q} </tex-math></inline-formula>, we obtain many minimal linear codes, which generalizes results of [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018] and [IEEE Trans. Inf. Theory, vol. 65, no. 11, pp. 7067-7078, 2019]. Finally, we use characteristic functions to present a characterization of minimal linear codes from the defining set method and present a class of minimal linear codes.]]></description><subject>Binary codes</subject><subject>Binary system</subject><subject>Boolean functions</subject><subject>characteristic function</subject><subject>Characteristic functions</subject><subject>Codes</subject><subject>Cryptography</subject><subject>Electronic mail</subject><subject>Frequency modulation</subject><subject>Hamming weight</subject><subject>Linear codes</subject><subject>Mathematics</subject><subject>Minimal linear code</subject><subject>subspace</subject><subject>Subspaces</subject><subject>weight distribution</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kM9LwzAUx4MoOKd3wUvBk4fOvPxokuMozg0qXnoPaZqyjK2dSSf435vRsdPjPT7fL48PQs-AFwBYvdebekEwwQuihKRS3KAZcC5yVXB2i2YYg8wVY_IePcS4SyvjQGaIfPneH8w-q3zvTMjKoXUxW4XhkJVbE4wdXfBx9DZbnXo7-qGPj-iuM_voni5zjurVR12u8-r7c1Muq9xSwse8BaBNJ6ChlAMUjcQtCO5s2zHMuOps6ygopzhRqrHCYSMawYVipiO0aOkcvU21W7PXx5CeDH96MF6vl5U-3zBVghIJv5DY14k9huHn5OKod8Mp9Ok7TRgtCoIl8EThibJhiDG47loLWJ8l6iRRnyXqi8QUeZki3jl3xRUmHCSm_0WHauA</recordid><startdate>20200901</startdate><enddate>20200901</enddate><creator>Mesnager, Sihem</creator><creator>Qi, Yanfeng</creator><creator>Ru, Hongming</creator><creator>Tang, Chunming</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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This paper uses characteristic functions of some subsets of <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{q} </tex-math></inline-formula> to construct minimal linear codes. By properties of characteristic functions, we can obtain more minimal binary linear codes from known minimal binary linear codes, which generalizes results of Ding et al. [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018]. By characteristic functions corresponding to some subspaces of <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{q} </tex-math></inline-formula>, we obtain many minimal linear codes, which generalizes results of [IEEE Trans. Inf. Theory, vol. 64, no. 10, pp. 6536-6545, 2018] and [IEEE Trans. Inf. Theory, vol. 65, no. 11, pp. 7067-7078, 2019]. Finally, we use characteristic functions to present a characterization of minimal linear codes from the defining set method and present a class of minimal linear codes.]]></abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TIT.2020.2978387</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0003-1381-5471</orcidid><orcidid>https://orcid.org/0000-0001-9599-851X</orcidid><orcidid>https://orcid.org/0000-0003-4008-2031</orcidid></addata></record> |
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| subjects | Binary codes Binary system Boolean functions characteristic function Characteristic functions Codes Cryptography Electronic mail Frequency modulation Hamming weight Linear codes Mathematics Minimal linear code subspace Subspaces weight distribution |
| title | Minimal Linear Codes From Characteristic Functions |
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