基于域 Fpm上一类特殊的矩阵，定义了环 R（pm，k）＝Fpm[u]／〈uk〉到 Fp j pm的一个新的 Gray 映射，其中 uk ＝0、p 为素数、j为正整数且 pj－1＋1≤k≤pj．得到了环 R（pm，k）上码长为任意长度 N 的（1＋u）常循环码的 Gray 象是 Fpm上长为 pjN 的保距线性循环码，并给出了 Gray 象的生成多项式，构造了 F3，F5和 F7上的一些最优线性循环码．%Let R(pm,k)denote the polynomial residue ring Fpm[u]/〈uk〉,where pj-1 +1 ≤k≤pj and uk =0 for some posi-tive prime number p and positive integer j.Based on a kind of matrix over Fpm ,a new Gray map from R(pm,k)to Fp j pm is defined.It is proved that the Gray image of a linear (1 +u)constacyclic code of an arbitrary length N over R(pm,k)is a distance invariant linear cyclic code of length pjN over Fpm .Moreover,the generator polynomial of the Gray image of such a constacyclic code is determined, and some optimal linear cyclic codes over F3,F5 and F7 are constructed via the Gray map.
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