On the Gray Images of Some Linear Codes and Quantum Codes - Dertli, A.; Çengellenmiş, Y. (Palestine Polytechnic University, 2020)
In this paper, we study the structures of cyclic, quasi-cyclic, constacyclic codes and their skew codes over the finite ring Sp = Fp + uFp + vFp, u2 = u; v2 = v; uv = vu = 0. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic and skew constacyclic codes over Sp are obtained. A necessary and sufficient condition for cyclic (negacyclic) codes over Sp 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.
Keywords: Constacyclic Codes; Cyclic Codes; Finite Rings; Quantum Codes; Quasi-Cyclic Codes; Skew Codes