2-D skew-cyclic codes over F_q[x,y;ρ,θ]

摘要

Let F_q be a finite field, p and 8 are two automorphisms of F_q· A ring structure on the set F_q[x,y;ρ,θ]= {∑∑a_(ij)x~iy~j |a_(ij)∈ F_q} is considered. As a generalization of 2-D cyclic codes, we propose 2-D skew-cyclic codes and prove that a 2-D skew-cyclic code is equivalent to a left F_q[x, y; ρ,θ]-submodule of the left F_q[x, y; ρ,θ]-module F_q[x, y; ρ,θ]/﹤x~s-1,y~l-1﹥_l. where ﹤x~s-1,y~l-1﹥_l is the left ideal generated by xx~s-1 and y~l-1. We introduce consistent systems in the bivariate skew polynomial ring and present some applications on 2-D skew-cyclic codes. In addition, relationships between 2-D skew-cyclic codes and 2-D cyclic codes and skew-cyclic codes are presented.