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Math."],"published-print":{"date-parts":[[2025,7]]},"abstract":"Abstract<\/jats:title>\n In this study, we introduce \n \n $$\\mathbb {F}_2$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n \n \n $$\\mathbb {F}_4$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-skew cyclic codes as a generalization of skew cyclic codes over \n \n $$\\mathbb {F}_4$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>. We characterize algebraic structures of \n \n $$\\mathbb {F}_2$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n \n \n $$\\mathbb {F}_4$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-skew cyclic codes by determining their generating polynomials and minimal spanning sets. We also exhibit generator matrices for these codes. Furthermore, we examine the duals of \n \n $$\\mathbb {F}_2$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n \n \n $$\\mathbb {F}_4$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-skew cyclic codes concerning a certain inner product and identify their generating polynomials. Finally, as an application of \n \n $$\\mathbb {F}_2$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n \n \n $$\\mathbb {F}_4$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-skew cyclic codes, we present some examples of near-MDS codes over \n \n $$\\mathbb {F}_4$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> and optimal binary linear codes which are Gray images of \n \n $$\\mathbb {F}_2$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n \n \n $$\\mathbb {F}_4$$<\/jats:tex-math>\n \n \n F<\/mml:mi>\n 4<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-skew cyclic codes.<\/jats:p>","DOI":"10.1007\/s40314-025-03226-7","type":"journal-article","created":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T17:48:57Z","timestamp":1746553737000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["$$\\mathbb {F}_2\\mathbb {F}_4$$-skew cyclic codes"],"prefix":"10.1007","volume":"44","author":[{"given":"Roghayeh Mohammadi","family":"Hesari","sequence":"first","affiliation":[]},{"given":"Mustafa","family":"Sari","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9308-4829","authenticated-orcid":false,"given":"Ismail","family":"Aydogdu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,6]]},"reference":[{"issue":"5","key":"3226_CR1","doi-asserted-by":"publisher","first-page":"2080","DOI":"10.1109\/TIT.2010.2044062","volume":"56","author":"T Abualrub","year":"2010","unstructured":"Abualrub T, Ghrayeb A, Aydin N, Siap I (2010) On the construction of skew quasi-cyclic codes. 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