环F2m+uF2m+u2F2m+u3F2m上线性码及其对偶码的Gray像

摘要

本文研究了环F2m+uF2m+u2 Fm+u3F2m上线性码.利用环是Frobenius环,证明了环上线性码C及其自对偶码的Gray像为F2m上的线性码和自对偶码.同时,给出了上循环码C的Gray像ψ(C)为F2m上的拟循环码.%The linear codes over F2m + uF2m + u2F2m + u3F2m are studied.Based on the fact that this ring is a Frobenius ring,the proposition that linear codes ψ(C⊥) are the dual codes of ψ(C) are shown.By using this proposition,the necessary and sufficient condition for a linear code over F2m + uF2m + u2F2m + u3F2m to be self-dual is obtained.Finally,the Gray image ψ(C) of cyclic codes C over F2m + uF2m + u2F2m + u3F2m are the quasi cyclic codes over F2m are showed.