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Codes Cryptogr."],"published-print":{"date-parts":[[2024,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce quaternary modified four <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mu $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03bc<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-circulant codes as a modification of four circulant codes. We give basic properties of quaternary modified four <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mu $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03bc<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-circulant Hermitian self-dual codes. We also construct quaternary modified four <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mu $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03bc<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-circulant Hermitian self-dual codes having large minimum weights. Two quaternary Hermitian self-dual [56,\u00a028,\u00a016] codes are constructed for the first time. These codes improve the previously known lower bound on the largest minimum weight among all quaternary (linear) [56,\u00a028] codes. In addition, these codes imply the existence of a quantum [[56,\u00a00,\u00a016]] code.<\/jats:p>","DOI":"10.1007\/s10623-024-01421-x","type":"journal-article","created":{"date-parts":[[2024,5,21]],"date-time":"2024-05-21T08:01:31Z","timestamp":1716278491000},"page":"2927-2948","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A method for constructing quaternary Hermitian self-dual codes and an application to quantum codes"],"prefix":"10.1007","volume":"92","author":[{"given":"Masaaki","family":"Harada","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,21]]},"reference":[{"key":"1421_CR1","doi-asserted-by":"publisher","first-page":"1813","DOI":"10.1007\/s10623-022-01172-7","volume":"91","author":"M Araya","year":"2023","unstructured":"Araya M., Harada M.: Some restrictions on the weight enumerators of near-extremal ternary self-dual codes and quaternary Hermitian self-dual codes. 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