Self-dual codes and quadratic residue codes over the ring $\mathbb{Z}_9+u\mathbb{Z}_9$

Jian Gao; XianFang Wang; Fang-Wei Fu

Self-dual codes and quadratic residue codes over the ring $\mathbb{Z}_9+u\mathbb{Z}_9$

Information Theory 2015-01-05 v3 math.IT Rings and Algebras

Authors: Jian Gao , XianFang Wang , Fang-Wei Fu

Abstract

In this paper, we introduce a new definitions of the Gray weight and the Gray map for linear codes over $\mathbb{Z}_9+u\mathbb{Z}_9$ with $u^2=u$ . Some results on self-dual codes over this ring are investigated. Further, the structural properties of quadratic residue codes are also considered. Two self-dual codes with parameters $[22,11,5]$ and $[24,12,9]$ over $\mathbb{Z}_9$ are obtained.

Keywords

self-dual codes quadratic residue codes Gray map Gray weight linear codes ring $\mathbb{Z}_9+u\mathbb{Z}_9$

Cite

@article{arxiv.1405.3347,
  title  = {Self-dual codes and quadratic residue codes over the ring $\mathbb{Z}_9+u\mathbb{Z}_9$},
  author = {Jian Gao and XianFang Wang and Fang-Wei Fu},
  journal= {arXiv preprint arXiv:1405.3347},
  year   = {2015}
}

Comments

12 pages. arXiv admin note: substantial text overlap with arXiv:1402.6771

Self-dual codes and quadratic residue codes over the ring $\mathbb{Z}_9+u\mathbb{Z}_9$

Abstract

Keywords

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