MDS and AMDS symbol-pair codes constructed from repeated-root codes
Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against the pair errors in symbol-pair read channels. One of the central themes in symbol-error correction is the construction of maximal distance separable (MDS) symbol-pair codes that possess the largest possible pai...
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| creator | Tang, Xiuxin Luo, Rong |
| description | Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to
protect against the pair errors in symbol-pair read channels. One of the
central themes in symbol-error correction is the construction of maximal
distance separable (MDS) symbol-pair codes that possess the largest possible
pair-error correcting performance. Based on repeated-root cyclic codes, we
construct two classes of MDS symbol-pair codes for more general generator
polynomials and also give a new class of almost MDS (AMDS) symbol-pair codes
with the length $lp$. In addition, we derive all MDS and AMDS symbol-pair codes
with length $3p$, when the degree of the generator polynomials is no more than
10. The main results are obtained by determining the solutions of certain
equations over finite fields. |
| doi_str_mv | 10.48550/arxiv.2206.00462 |
| format | Article |
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protect against the pair errors in symbol-pair read channels. One of the
central themes in symbol-error correction is the construction of maximal
distance separable (MDS) symbol-pair codes that possess the largest possible
pair-error correcting performance. Based on repeated-root cyclic codes, we
construct two classes of MDS symbol-pair codes for more general generator
polynomials and also give a new class of almost MDS (AMDS) symbol-pair codes
with the length $lp$. In addition, we derive all MDS and AMDS symbol-pair codes
with length $3p$, when the degree of the generator polynomials is no more than
10. The main results are obtained by determining the solutions of certain
equations over finite fields.</description><identifier>DOI: 10.48550/arxiv.2206.00462</identifier><language>eng</language><subject>Computer Science - Information Theory ; Mathematics - Information Theory</subject><creationdate>2022-06</creationdate><rights>http://creativecommons.org/licenses/by-sa/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2206.00462$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2206.00462$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Tang, Xiuxin</creatorcontrib><creatorcontrib>Luo, Rong</creatorcontrib><title>MDS and AMDS symbol-pair codes constructed from repeated-root codes</title><description>Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to
protect against the pair errors in symbol-pair read channels. One of the
central themes in symbol-error correction is the construction of maximal
distance separable (MDS) symbol-pair codes that possess the largest possible
pair-error correcting performance. Based on repeated-root cyclic codes, we
construct two classes of MDS symbol-pair codes for more general generator
polynomials and also give a new class of almost MDS (AMDS) symbol-pair codes
with the length $lp$. In addition, we derive all MDS and AMDS symbol-pair codes
with length $3p$, when the degree of the generator polynomials is no more than
10. The main results are obtained by determining the solutions of certain
equations over finite fields.</description><subject>Computer Science - Information Theory</subject><subject>Mathematics - Information Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8luwjAQhn3poaI8QE_1CzgdL3HwEaVsEogD3KOxY0uRCI6cFMHbE5bLv-gfjfQR8s0hU7M8h19M1-aSCQE6A1BafJJy93egeK7p_BH6W2vjiXXYJOpi7ftRz_2Q_t3gaxpSbGnyncexsRTj8Dr6Ih8BT72fvn1CjsvFsVyz7X61KedbhroQTBYCjQ_GcoegjFIYguRSKXDO6hyE1SYYaWqjcw7awjhrgGIWpHQFd3JCfl5vnxRVl5oW06160FRPGnkHUE9DiA</recordid><startdate>20220601</startdate><enddate>20220601</enddate><creator>Tang, Xiuxin</creator><creator>Luo, Rong</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220601</creationdate><title>MDS and AMDS symbol-pair codes constructed from repeated-root codes</title><author>Tang, Xiuxin ; Luo, Rong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a672-372a9ef9b1ca04944aff313440ccb6502b69f939d965106b0ff360078f33c71c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Computer Science - Information Theory</topic><topic>Mathematics - Information Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Tang, Xiuxin</creatorcontrib><creatorcontrib>Luo, Rong</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Tang, Xiuxin</au><au>Luo, Rong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>MDS and AMDS symbol-pair codes constructed from repeated-root codes</atitle><date>2022-06-01</date><risdate>2022</risdate><abstract>Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to
protect against the pair errors in symbol-pair read channels. One of the
central themes in symbol-error correction is the construction of maximal
distance separable (MDS) symbol-pair codes that possess the largest possible
pair-error correcting performance. Based on repeated-root cyclic codes, we
construct two classes of MDS symbol-pair codes for more general generator
polynomials and also give a new class of almost MDS (AMDS) symbol-pair codes
with the length $lp$. In addition, we derive all MDS and AMDS symbol-pair codes
with length $3p$, when the degree of the generator polynomials is no more than
10. The main results are obtained by determining the solutions of certain
equations over finite fields.</abstract><doi>10.48550/arxiv.2206.00462</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Information Theory Mathematics - Information Theory |
| title | MDS and AMDS symbol-pair codes constructed from repeated-root codes |
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