环F_q+vF_q+v^2F_q+v^3F_q上的交错循环码

Skew cyclic codes over F_q+vF_q+v^2F_q+v^3F_q

在环R=F_q+vF_q+v^2F_q+v^3F_q上研究交错循环码,其中q=pr,p是一个素数,3 p(-1).通过建立从Rn到Fq4n的保持自对偶性的Gray映射,由分解定理可以确定环R上交错循环码的生成多项式和幂等生成元.最终可得到环R上交错循环码的对偶码的生成多项式.

Skew cyclic codes over R=Fq＋vFq＋v^2Fq＋v^3Fq are studied, where q=p^r,p is a prime and 3｜ （p - 1） . A Gray map preserving the property of self-duality from R^n to Fq^4n is given. The generator polynomials and generating idempotent of skew cyclic codes over R are described by a decomposition theorem. The generator polynomials of the dual codes of skew cyclic codes over R are also obtained.