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Appl. Math."],"published-print":{"date-parts":[[2026,5]]},"abstract":"Abstract<\/jats:title>\n \n We introduce homothetic-BCH codes. These are a family of\n \n \n $$q^2$$<\/jats:tex-math>\n \n \n q<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -ary classical codes\n \n \n $$\\mathcal {C}$$<\/jats:tex-math>\n \n C<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n of length\n \n \n $$\\lambda n_1$$<\/jats:tex-math>\n \n \n \u03bb<\/mml:mi>\n \n n<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , where\n \n \n $$\\lambda $$<\/jats:tex-math>\n \n \u03bb<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and\n \n \n $$n_1$$<\/jats:tex-math>\n \n \n n<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n are suitable positive integers such that the punctured code\n \n \n $$\\mathcal {B}$$<\/jats:tex-math>\n \n B<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n of\n \n \n $$\\mathcal {C}$$<\/jats:tex-math>\n \n C<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n in the last\n \n \n $$\\lambda n_1 -n_1$$<\/jats:tex-math>\n \n \n \u03bb<\/mml:mi>\n \n n<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n -<\/mml:mo>\n \n n<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n coordinates is a narrow-sense BCH code of length\n \n \n $$n_1$$<\/jats:tex-math>\n \n \n n<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n . We prove that whenever\n \n \n $$\\mathcal {B}$$<\/jats:tex-math>\n \n B<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is Hermitian self-orthogonal, so is\n \n \n $$\\mathcal {C}$$<\/jats:tex-math>\n \n C<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n . As a consequence, we present a procedure to obtain quantum stabilizer codes with lengths that cannot be reached by BCH codes. With this procedure, we get new quantum codes according to Grassl\u2019s table (Grassl 2025). To prove our results, we give necessary and sufficient conditions for Hermitian self-orthogonality of BCH codes of a wide range of lengths.\n <\/jats:p>","DOI":"10.1007\/s40314-025-03570-8","type":"journal-article","created":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T07:40:27Z","timestamp":1766043627000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["New quantum codes from homothetic-BCH codes"],"prefix":"10.1007","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3908-4462","authenticated-orcid":false,"given":"C.","family":"Galindo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9758-2152","authenticated-orcid":false,"given":"F.","family":"Hernando","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6379-6902","authenticated-orcid":false,"given":"H.","family":"Mart\u00edn-Cruz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,12,18]]},"reference":[{"issue":"3","key":"3570_CR1","doi-asserted-by":"publisher","first-page":"1183","DOI":"10.1109\/TIT.2006.890730","volume":"53","author":"SA Aly","year":"2007","unstructured":"Aly SA, Klappenecker A, Sarvepalli PK (2007) On quantum and classical BCH codes. 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