F2F4-skew cyclic codes

Abstract

In this study, we introduce F2F4-skew cyclic codes as a generalization of skew cyclic codes over F-4. We characterize algebraic structures of F2F4-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 F2F4-skew cyclic codes concerning a certain inner product and identify their generating polynomials. Finally, as an application of F2F4-skew cyclic codes, we present some examples of near-MDS codes over F-4 and optimal binary linear codes which are Gray images of F2F4-skew cyclic codes.