Optimal codes for correcting a single (wrap-around) burst of errors
In 2007, Martinian and Trott presented codes for correcting a burst of erasures with a minimum decoding delay. Their construction employs [n,k] codes that can correct any burst of erasures (including wrap-around bursts) of length n-k. The raised the question if such [n,k] codes exist for all integer...
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creator | Hollmann, Henk D. L Tolhuizen, Ludo M. G. M |
description | In 2007, Martinian and Trott presented codes for correcting a burst of
erasures with a minimum decoding delay. Their construction employs [n,k] codes
that can correct any burst of erasures (including wrap-around bursts) of length
n-k. The raised the question if such [n,k] codes exist for all integers k and n
with 1 |
doi_str_mv | 10.48550/arxiv.0712.2182 |
format | Article |
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erasures with a minimum decoding delay. Their construction employs [n,k] codes
that can correct any burst of erasures (including wrap-around bursts) of length
n-k. The raised the question if such [n,k] codes exist for all integers k and n
with 1<= k <= n and all fields (in particular, for the binary field). In this
note, we answer this question affirmatively by giving two recursive
constructions and a direct one.</description><identifier>DOI: 10.48550/arxiv.0712.2182</identifier><language>eng</language><subject>Computer Science - Information Theory ; Mathematics - Information Theory</subject><creationdate>2007-12</creationdate><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/0712.2182$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.0712.2182$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Hollmann, Henk D. L</creatorcontrib><creatorcontrib>Tolhuizen, Ludo M. G. M</creatorcontrib><title>Optimal codes for correcting a single (wrap-around) burst of errors</title><description>In 2007, Martinian and Trott presented codes for correcting a burst of
erasures with a minimum decoding delay. Their construction employs [n,k] codes
that can correct any burst of erasures (including wrap-around bursts) of length
n-k. The raised the question if such [n,k] codes exist for all integers k and n
with 1<= k <= n and all fields (in particular, for the binary field). In this
note, we answer this question affirmatively by giving two recursive
constructions and a direct one.</description><subject>Computer Science - Information Theory</subject><subject>Mathematics - Information Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotjztPwzAURr0woMLOVHmEIeH6FTsjinhJlbp0j65jG0UKdXSd8vj3pMB0vunTOYzdCKi1Mwbukb7GjxqskLUUTl6ybj8v4ztOfMghFp4yrYsoDst4fOPIy4op8ttPwrlCyqdjuOP-RGXhOfFIlKlcsYuEU4nX_9yww9PjoXupdvvn1-5hV2FjZNVYkN4ZhTjYNqADaI3TwXoRICqlvG48eCn0aorWo496aIxQQUObQCS1Ydu_29-IfqbVm777c0x_jlE_NtJDnA</recordid><startdate>20071213</startdate><enddate>20071213</enddate><creator>Hollmann, Henk D. L</creator><creator>Tolhuizen, Ludo M. G. M</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20071213</creationdate><title>Optimal codes for correcting a single (wrap-around) burst of errors</title><author>Hollmann, Henk D. L ; Tolhuizen, Ludo M. G. M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a652-6702b853aac79da8009584d7b1d0e333b46b0b214485a7babe4c6513d409f01f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Computer Science - Information Theory</topic><topic>Mathematics - Information Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Hollmann, Henk D. L</creatorcontrib><creatorcontrib>Tolhuizen, Ludo M. G. M</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>Hollmann, Henk D. L</au><au>Tolhuizen, Ludo M. G. M</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimal codes for correcting a single (wrap-around) burst of errors</atitle><date>2007-12-13</date><risdate>2007</risdate><abstract>In 2007, Martinian and Trott presented codes for correcting a burst of
erasures with a minimum decoding delay. Their construction employs [n,k] codes
that can correct any burst of erasures (including wrap-around bursts) of length
n-k. The raised the question if such [n,k] codes exist for all integers k and n
with 1<= k <= n and all fields (in particular, for the binary field). In this
note, we answer this question affirmatively by giving two recursive
constructions and a direct one.</abstract><doi>10.48550/arxiv.0712.2182</doi><oa>free_for_read</oa></addata></record> |
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subjects | Computer Science - Information Theory Mathematics - Information Theory |
title | Optimal codes for correcting a single (wrap-around) burst of errors |
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