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

Jian Gao; XianFang Wang; Fang-Wei Fu

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arXiv · 1405.3347

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

Jian Gao·XianFang Wang·Fang-Wei Fu

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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.

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Jian Gao, XianFang Wang, Fang-Wei Fu. 2014-05-14. Self-dual codes and quadratic residue codes over the ring $\mathbb{Z}_9+u\mathbb{Z}_9$. https://arxiv.org/abs/1405.3347

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