{"pk":64993,"title":"Two constructions of quaternary Legendre pairs of even length","subtitle":null,"abstract":"We give the first general constructions of even length quaternary Legendre pairs: there is a quaternary Legendre pair of length \\((q-1)/2\\) for every prime power \\(q\\) congruent to \\(1\\) modulo \\(4\\), and there is a quaternary Legendre pair of length \\(2p\\) for every odd prime \\(p\\) for which \\(2p-1\\) is a prime power.\n \nMathematics Subject Classifications: 05B20, 05B30\n \nKeywords: Legendre pair, quaternary Legendre pair, Goethals-Seidel sequences, Hadamard matrix","language":"en","license":{"name":"Creative Commons Attribution 4.0","short_name":"CC BY 4.0","text":"Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.","url":"https://creativecommons.org/licenses/by/4.0"},"keywords":[{"word":"Legendre pair"},{"word":"quaternary Legendre pair"},{"word":"Goethals-Seidel sequences"},{"word":"Hadamard matrix"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/71m2d1sj","frozenauthors":[{"first_name":"Jonathan","middle_name":"","last_name":"Jedwab","name_suffix":"","institution":"Department of Mathematics, Simon Fraser University, Burnaby BC V5A 1S6, Canada","department":""},{"first_name":"Thomas","middle_name":"","last_name":"Pender","name_suffix":"","institution":"Department of Mathematics, Simon Fraser University, Burnaby BC V5A 1S6, Canada","department":""}],"date_submitted":"2025-07-15T15:35:07Z","date_accepted":"2025-07-15T15:35:07Z","date_published":"2025-07-15T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64993/galley/49803/download/"}]}