English

On Linear Codes over $\mathbb{Z}_4+v\mathbb{Z}_4$

Information Theory 2015-01-05 v2 math.IT

Abstract

Linear codes are considered over the ring Z4+vZ4\mathbb{Z}_4+v\mathbb{Z}_4, where v2=vv^2=v. Gray weight, Gray maps for linear codes are defined and MacWilliams identity for the Gray weight enumerator is given. Self-dual codes, construction of Euclidean isodual codes, unimodular complex lattices, MDS codes and MGDS codes over Z4+vZ4\mathbb{Z}_4+v\mathbb{Z}_4 are studied. Cyclic codes and quadratic residue codes are also considered. Finally, some examples for illustrating the main work are given.

Keywords

Cite

@article{arxiv.1402.6771,
  title  = {On Linear Codes over $\mathbb{Z}_4+v\mathbb{Z}_4$},
  author = {Jian Gao and Yun Gao and Fang-Wei Fu},
  journal= {arXiv preprint arXiv:1402.6771},
  year   = {2015}
}

Comments

25 pages

R2 v1 2026-06-22T03:16:47.920Z