{"title":"Conjectural permutation decoding of some AG codes","authors":"D. Joyner","doi":"10.1145/1080368.1080374","DOIUrl":null,"url":null,"abstract":"We study the action of a finite group on the Riemann-Roch space of certain divisors on a specific hyperelliptic curve <i>X</i> defined over a finite field with \"large\" automorphism group <i>G</i>. If <i>D</i> and <i>E</i> = <i>P</i><inf>l</inf> + ... + <i>P<inf>n</inf></i> are <i>G</i>-equivariant divisors on <i>X</i> (<i>P<inf>i</inf></i> ∈ <i>X</i>(<i>F</i>)) then <i>G</i> acts on associated AG code <i>C</i> = <i>C</i>(<i>D,E</i>) by permuting coordinates. This note discusses the permutation decoding of these AG codes. The main \"results\" are conjectures regarding the complexity of the permutation decoding of these hyperelliptic codes. The open source GAP error-correcting codes package GUAVA is used to compute examples.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"98 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIGSAM Bull.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1080368.1080374","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9
Abstract
We study the action of a finite group on the Riemann-Roch space of certain divisors on a specific hyperelliptic curve X defined over a finite field with "large" automorphism group G. If D and E = Pl + ... + Pn are G-equivariant divisors on X (Pi ∈ X(F)) then G acts on associated AG code C = C(D,E) by permuting coordinates. This note discusses the permutation decoding of these AG codes. The main "results" are conjectures regarding the complexity of the permutation decoding of these hyperelliptic codes. The open source GAP error-correcting codes package GUAVA is used to compute examples.
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