{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:42:34Z","timestamp":1750308154482,"version":"3.41.0"},"reference-count":14,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2005,3,1]],"date-time":"2005-03-01T00:00:00Z","timestamp":1109635200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSAM Bull."],"published-print":{"date-parts":[[2005,3]]},"abstract":"<jats:p>\n            We study the action of a finite group on the Riemann-Roch space of certain divisors on a specific hyperelliptic curve\n            <jats:italic>X<\/jats:italic>\n            defined over a finite field with \"large\" automorphism group\n            <jats:italic>G<\/jats:italic>\n            . If\n            <jats:italic>D<\/jats:italic>\n            and\n            <jats:italic>E<\/jats:italic>\n            =\n            <jats:italic>P<\/jats:italic>\n            <jats:sub>l<\/jats:sub>\n            + ... +\n            <jats:italic>\n              P\n              <jats:sub>n<\/jats:sub>\n            <\/jats:italic>\n            are\n            <jats:italic>G<\/jats:italic>\n            -equivariant divisors on\n            <jats:italic>X<\/jats:italic>\n            (\n            <jats:italic>\n              P\n              <jats:sub>i<\/jats:sub>\n            <\/jats:italic>\n            \u2208\n            <jats:italic>X<\/jats:italic>\n            (\n            <jats:italic>F<\/jats:italic>\n            )) then\n            <jats:italic>G<\/jats:italic>\n            acts on associated AG code\n            <jats:italic>C<\/jats:italic>\n            =\n            <jats:italic>C<\/jats:italic>\n            (\n            <jats:italic>D,E<\/jats:italic>\n            ) 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.\n          <\/jats:p>","DOI":"10.1145\/1080368.1080374","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"26-32","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Conjectural permutation decoding of some AG codes"],"prefix":"10.1145","volume":"39","author":[{"given":"David","family":"Joyner","sequence":"first","affiliation":[{"name":"US Naval Academy, Annapolis, MD"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2005,3]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"{G} N. G\u00f6b \"Computing the automorphism groups of hyperelliptic function fields \" available at http:\/\/front.math.ucdavis.edu\/math.NT\/0305284.  {G} N. G\u00f6b \"Computing the automorphism groups of hyperelliptic function fields \" available at http:\/\/front.math.ucdavis.edu\/math.NT\/0305284."},{"key":"e_1_2_1_2_1","unstructured":"{GUAVA} GUAVA package for GAP 4.4 (http:\/\/www.gap-system.org) available at http:\/\/cadigweb.ew.usna.edu\/~wdj\/gap\/GUAVA\/or http:\/\/www.gap-system.org\/Packages\/guava.html  {GUAVA} GUAVA package for GAP 4.4 (http:\/\/www.gap-system.org) available at http:\/\/cadigweb.ew.usna.edu\/~wdj\/gap\/GUAVA\/or http:\/\/www.gap-system.org\/Packages\/guava.html"},{"key":"e_1_2_1_3_1","volume-title":"private communication","author":"Guralnick R.","year":"2004","unstructured":"{Gu} R. Guralnick , private communication , 2004 . {Gu} R. 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Brualdi Eds.), Elsevier, Amsterdam 1998."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511807077"},{"key":"e_1_2_1_7_1","unstructured":"{JK1} D. Joyner and A. Ksir \"Automorphism groups of some AG codes\" available at http:\/\/front.math.ucdavis.edu\/math.AG\/0412459  {JK1} D. Joyner and A. Ksir \"Automorphism groups of some AG codes\" available at http:\/\/front.math.ucdavis.edu\/math.AG\/0412459"},{"key":"e_1_2_1_8_1","unstructured":"{JK2} D. Joyner and A. Ksir \"Representations of finite groups on Riemann-Roch spaces II \" available at http:\/\/front.math.ucdavis.edu\/math.AG\/0312383  {JK2} D. Joyner and A. Ksir \"Representations of finite groups on Riemann-Roch spaces II \" available at http:\/\/front.math.ucdavis.edu\/math.AG\/0312383"},{"key":"e_1_2_1_9_1","unstructured":"{JT} D. Joyner and W. Traves \"Representations of finite groups on Riemann-Roch spaces\" available at http:\/\/front.math.ucdavis.edu\/math.AG\/0210408  {JT} D. Joyner and W. 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