环Fpmu/<uk>上一类常循环码的Gray像

环Fpmu/上一类常循环码的Gray像

摘要: 令R(pm,k)=Fpm［u］/，其中pj－1+1≤k≤pj、uk=0、p为正素数、j为正整数. 定义了从R(pm,k)到Fpmpj的一个新的Gray映射，得到了环R(pm,k)上码长为任意长度N的线性(1+u+…+uk－1)常循环码的Gray像是Fpm上长为pjN的保距线性循环码，并给出了Gray像的生成多项式，构造了F3, F5 和F7上的一些最优线性循环码.

Abstract: Let R(pm,k)=Fpm［u］/, where pj－1+1≤k≤pj and uk=0 for some positive prime number p and positive integer j. A new Gray map from R(pm,k) to Fpmpj was defined. It was proved that the Gray image of a linear (1+u+…+uk－1) constacyclic code of an arbitrary length N over R(pm,k) is a distance invariant linear cyclic code of length pjN over Fpm. Moreover, the generator polynomial of the Gray image of such a constacyclic code was determined, and some optimal linear cyclic codes over F3, F5 and F7 were constructed via the Gray map.