CONSTACYCLIC CODES OF ARBITRARY LENGTHS OVER RING Z_(p^m) +vZ_(p^m)

By constructing a Gray map, constacyclic codes of arbitrary lengths over ring R =Z p m +vZ pmare studied, wherev 2=v. The structure of constacyclic codes over R and their dual codes are obtained. A necessary and sufficient condition for a linear code to be self-dual constacyclic is given. In particular,(1 +(v +1)ap)-constacyclic codes over R are classified in terms of generator polynomial, where a is a unit of Z m.

Constacyclic Codes of Length Ps over Finite Rings FPm+uFPm+vFPm+uvFPm

Let R-Fpm+uFpm+vFpm+uvFpm,where u2=v2=0,uv=vu.Then R is a local ring,but it is not a chain ring.R contains precisely(pm-1)p3 m units,namely,α+uβ+vγ+uvδ,where α,β,γ,δ∈Fpm,α≠0.In this paper,we investigate all constacyclic codes of length ps over R.Firstly,we classify allα-constacyclic and(α+uvβ)-constacyclic codes of length ps over R,respectively,and obtain their structure in each of thoseα-constacyclic and(α+uvβ)-constacyclic codes.Secondly,we address the(α+uβ)-constacyclic codes of length ps over R,and get their classification and structure.Finally,using similar discussion of(α+uβ)-constacyclic codes,we obtain the classification and the structure of α+vβ,α+uβ+uvγ,α+vβ+uvγ,α+uβ+vγ,α+uβ+vβ+uvδ-constacyclic codes of length ps over R.

Ranks of Repeated-Root Constacyclic Code

By the discussion of division in F2m[u]/〈u4〉,the minimal spanning set and the rank of a（1＋u＋u2）-constacyclic code with an arbitrary length N=2en over F2m[u]/〈u4〉 are determined based on the factorization of（xn-1） over F2m.

Constacyclic and cyclic codes over finite chain rings

The problem of Gray image of constacyclic code over finite chain ring is studied. A Gray map between codes over a finite chain ring and a finite field is defined. The Gray image of a linear constacyclic code over the finite chain ring is proved to be a distance invariant quasi-cyclic code over the finite field. It is shown that every code over the finite field, which is the Gray image of a cyclic code over the finite chain ring, is equivalent to a quasi-cyclic code.

Chinese product of constacyclic and cyclic codes over finite rings

In this paper, we study the Gray images of the Chinese product of constacyclic and cyclic codes over a finite ring. We first introduce the Chinese product of constacyclic and cyclic codes over the finite ring. We then define a Gray map between codes over the finite ring and a finite field. We prove that the Gray image of the Chinese product of constacyclic codes over the finite ring is a distance-invariant quasi-cyclic code over the finite field. We also prove that each code over the finite field, which is the Gray image of the Chinese product of cyclic codes over the finite ring, is permutation equivalent to a quasi-cyclic code.

环F_(p)+vF_(p)+v^(2)F_(p)上常循环码的深度分布

In this paper,we studied the depth spectrum and the depth distribution of constacyclic codes over the non-chain ring R=F_(p)+vF_(p)+v^(2)F_(p),where v^(3)=v.By decomposing the linear codes C over R into the linear codes over the finite field F_(p),three corresponding constacyclic codes C_(1),C_(2),C_(3) over F_(p)were obtained.Furthermore,considering the depth spectrum of constacyclic codes over the finite filed F_(p),and the relationship between constacyclic codes C_(1),C_(2),C_(3) and C,the depth spectrum and the depth distribution of constacyclic codes over R were discussed.

A Note on Skew Cyclic Codes over a Class of Rings

We study skew cyclic codes over a class of rings R=F0■F1■⋯■Ft−1,where each Fi(i=0,…,t−1)is a finite field.We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R.Moreover,we discuss possible extension of our results in the more general setting ofδR-dual skew constacyclic codes over R,whereδR is an automorphism of R.