Year: 2025
Type: article
Abstract: In this study, we introduce $$\mathbb {F}_2$$ F 2 $$\mathbb {F}_4$$ F 4 -skew cyclic codes as a generalization of skew cyclic codes over $$\mathbb {F}_4$$ F 4 . We characterize algebraic structures of $$\mathbb {F}_2$$ F 2 $$\mathbb {F}_4$$ F 4 -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 $$\mathbb {F}_2$$ F 2 $$\mathbb {F}_4$$ F 4 -skew cyclic codes concerning a certain inner product and identify their generating polynomials. Finally, as an application of $$\mathbb {F}_2$$ F 2 $$\mathbb {F}_4$$ F 4 -skew cyclic codes, we present some examples of near-MDS codes over $$\mathbb {F}_4$$ F 4 and optimal binary linear codes which are Gray images of $$\mathbb {F}_2$$ F 2 $$\mathbb {F}_4$$ F 4 -skew cyclic codes.
Institutions: Payame Noor University, Yıldız Technical University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,390
OpenAlex ID: W4410106597