Some results on <inline-formula><tex-math id="M1111">\begin{document}$ \mathbb{Z}_p\mathbb{Z}_p[v] $\end{document}</tex-math></inline-formula>-additive cyclic codes

Abstract

ZpZp[v]-Additive cyclic codes of length (α, β) can be viewed as R[x]-submodules of Zp[x]/(x α − 1) × R[x]/(x β − 1), where R = Zp + vZp with v 2 = v. In this paper, we determine the generator polynomials and the minimal generating sets of this family of codes as R[x]-submodules of Zp[x]/(x α − 1) × R[x]/(x β − 1). We also determine the generator polynomials of the dual codes of ZpZp[v]-additive cyclic codes. Some optimal ZpZp[v]-linear codes and MDSS codes are obtained from ZpZp[v]-additive cyclic codes. Moreover, we also get some quantum codes from ZpZp[v]-additive cyclic codes.

A Study of FqR-Cyclic Codes and Their Applications in Constructing Quantum Codes

“…Let f (x) = (x + 2)(x 2 + 3x + 3). Then C r = f (x)is a cyclic code over F 5 with parameters[24,21,3]. Note that f * (x) = (x + 3)(x 2 + x + 2).…”