环F_(p^m)+uF_(p^m)+vF_(p^m)+uvF_(p^m)上的一类重根常循环码

A FAMILY OF REPEATED-ROOT CONSTACYCLIC CODES OVER F_(p^m)+uF_(p^m)+vF_(p^m)+uvF_(p^m)

对环F_pm+uF_pm+uF_pm+uvF_pm上长为P^e的所有(a+uβ)-循环码进行了分类,其中产~2=0,v^2=0,uv=vu,α,β∈F_p~*m.对于给定的α,β,e,我们得到了该环上长为P^e的所有(α+uβ)-循环码的计数公式.最后定义了这些常循环码的扭码和剩余码,并利用扭码获得了该环上长为P^e的(α+uβ)-循环码的Hamming距离分布.

In this paper,we classify all （α ＋ βu）-cyclic codes of length pe over Fpm ＋ uFpm ＋ vFpm ＋ uvFpm,where u2 =0,v2 =0,uv =vu,α,β ∈ F＊ppm.For any given α,β,e,a formula for the number of these constacyclic codes is obtained.Then,the Torsion codes and Residue codes of those constacyclic codes are also defined.Finally,the Hamming distance distribution of those constacyclic codes is given with the help of their Torsion codes.