On the Gray Images of Some Linear Codes and Quantum Codes

Abstract

In this paper, we study the structures of cyclic, quasi-cyclic, constacyclic codes and their skew codes over the finite ring S<inf>p</inf> = F<inf>p</inf> + uF<inf>p</inf> + vF<inf>p</inf>, u2 = u; v2 = v; uv = vu = 0. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic and skew constacyclic codes over S<inf>p</inf> are obtained. A necessary and sufficient condition for cyclic (negacyclic) codes over S<inf>p</inf> that contains its dual has been given. The parameters of quantum error correcting codes are obtained from both cyclic and negacyclic codes over Sp. The MacWilliams identities are obtained. © Palestine Polytechnic University-PPU 2020.