English

On Codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$

Information Theory 2017-04-13 v1 math.IT Rings and Algebras

Abstract

In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring R=\Fq+v\Fq+v2\FqR=\F_{q}+v\F_{q}+v^{2}\F_{q}, where v3=vv^{3}=v, for qq odd. We give conditions on the existence of LCD codes and present construction of formally self-dual codes over RR. Further, we give bounds on the minimum distance of LCD codes over \Fq\F_q and extend these to codes over RR.

Keywords

Cite

@article{arxiv.1704.03519,
  title  = {On Codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$},
  author = {A. Melakhessou and K. Guenda and T. A. Gulliver and M. Shi and P. Solé},
  journal= {arXiv preprint arXiv:1704.03519},
  year   = {2017}
}

Comments

19 pages

R2 v1 2026-06-22T19:14:51.523Z