F_p+uF_p+vF_p上的一类常循环码

A family of constacyclic codes over F_p+uF_p+vF_p

文章研究了有限环R=F_p+uF_p+vF_p上任意长度的(1-u-v)-常循环码,其中u^2=v^2=0和uv=vu=0。利用同态映射给出了环R上任意长度的(1-u-v)-常循环码的结构,引入了一个从R到F2pp的Gray映射,证明了环R上长为n的(1-u-v)-常循环码的Gray象是F_p上长为2pn、指数为2的线性准循环码。

The （1 -u- v） -constacyclic codes of an vFp are studied, where u2 = v2 = 0 and uv= vu = O, arbitrary length over the finite ring R=Fp ＋uFp ＋ The structure of （1 - u - v） -constacyclic codes of an arbitrary length over the ring R is determined hy using a homomorphism. A Gray map fromR to Fp^2p is introduced. It is shown that the Gray image of a （1 - u- v） -constacyclic code over R of length n is a linear quasi-cyclic code of length 2pn and index 2 over Fp.