{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:14Z","timestamp":1753894394255,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Combinatorics","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Combinatorics<\/jats:p>\n          <jats:p xml:lang=\"en\">For an odd prime p and each non-empty subset S \u2282 GF(p), consider the hyperelliptic curve X_S de\ufb01ned by y^2 = f_s(x), where f_s(x) = \\P_{a2S} (x-a). Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p), this paper investigates how coding theory bounds give rise to bounds such as the following example: for all suf\ufb01ciently large primes p there exists a subset S \u2282 GF(p) for which the bound |X_S(GF(p))| &gt; 1.39p holds. We also use the quasi-quadratic residue codes de\ufb01ned below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the \"Riemann hypothesis.\"<\/jats:p>","DOI":"10.46298\/dmtcs.429","type":"journal-article","created":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T21:40:19Z","timestamp":1629754819000},"source":"Crossref","is-referenced-by-count":0,"title":["On quadratic residue codes and hyperelliptic curves"],"prefix":"10.46298","volume":"Vol. 10 no. 1","author":[{"given":"David","family":"Joyner","sequence":"first","affiliation":[{"name":"Mathematics Department [UNSA Annapolis]"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2008,1,1]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dmtcs.episciences.org\/429\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dmtcs.episciences.org\/429\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T19:47:35Z","timestamp":1687290455000},"score":1,"resource":{"primary":{"URL":"https:\/\/dmtcs.episciences.org\/429"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1,1]]},"references-count":0,"journal-issue":{"issue":"Combinatorics","published-online":{"date-parts":[[2008,1,1]]}},"URL":"https:\/\/doi.org\/10.46298\/dmtcs.429","relation":{"is-same-as":[{"id-type":"uri","id":"https:\/\/hal.science\/hal-00972302v1","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"type":"electronic","value":"1365-8050"}],"subject":[],"published":{"date-parts":[[2008,1,1]]},"article-number":"429"}}