Liqin Qian

Good self-dual generalized quasi-cyclic codes exist

We show that there are good long binary generalized quasi-cyclic self-dual (either Type I or Type II) codes.

On constacyclic codes over Z4[u]/〈u2−1〉 and their Gray images

Abstract We first define a new Gray map from R = Z 4 + u Z 4 to Z 4 2 , where u 2 = 1 and study ( 1 + 2 u ) -constacyclic codes over R. Also of interest are some properties of ( 1 + 2 u ) -constacyclic codes over R. Considering their Z 4 images, we prove that the Gray images of ( 1 + 2 u ) -constacyclic codes of length n over R are cyclic codes of length 2n over Z 4 . In many cases the latter codes have better parameters than those in the online database of Aydin and Asamov. We also give a corrected version of a table of new cyclic R-codes published by Ozen et al. [7] .

Few-weight codes from trace codes over a local ring

In this paper, few weights linear codes over the local ring

On self-dual and LCD quasi-twisted codes of index two over a special chain ring

R={\mathbb {F}}_p+u{\mathbb {F}}_p+v{\mathbb {F}}_p+uv{\mathbb {F}}_p,

On constacyclic codes over Z4[u]/〈u2−1〉Z4[u]/〈u2−1〉 and their Gray images

R=Fp+uFp+vFp+uvFp, with

Linear codes with few weights over

u^2=v^2=0, uv=vu,