环F_(p^m)+uF_(p^m)+vF_(p^m)上长为p^k的(β+γu)-常循环码

(β + γu)-Constacyclic Codes of Length pkover F_(p^m)+ uF_(p^m)+ vF_(p^m)

证明了R(x)=R[x]/〈x^(p^k)-(1+αu)〉不是主理想环,其中R=F_(p^m)+uF_(p^m)+vF_(p^m),u^2=0,v^2=0,uv=vu=0且α∈F_(p^m)*。分5种情形讨论了环R(x)中的理想,给出了R上长为p^k的(1+αu)-常循环码的可以唯一确定的生成元的表达形式。利用环同构,得到了R上长为pk的(β+γu)-常循环码的可以唯一确定的生成元的表达形式,其中β,γ∈F_(p^m)*。

R （ x ） = R [x ]/（ xpk - （ 1 ＋αu ） ） is not a principal ideal domain was proved in the paper, whereR = Fpm ＋uFpm ＋VFpm with u2 = 0,v2 = 0,uv= vu = 0 andα∈Fpm＊. Then, the ideals of R （ x ） were discussed in five cases and the expressions of the uniquely determined generators of the （ 1 ＋ αu） -constacy- clic codes were given. Finally, one to one correspondences between （ 1 ＋ αu） -constacyclic codes and （β＋γu）-constacyelic codes were provided via ring isomorphism, which allow us to carry over the results about （1 ＋ αu）-eonstacyclic codes accordingly to （β＋γu）-constacvclic codes.