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arXiv · 1402.6771

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

Jian Gao·Yun Gao·Fang-Wei Fu
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Abstract

Linear codes are considered over the ring $\mathbb{Z}_4+v\mathbb{Z}_4$, where $v^2=v$. 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 $\mathbb{Z}_4+v\mathbb{Z}_4$ are studied. Cyclic codes and quadratic residue codes are also considered. Finally, some examples for illustrating the main work are given.

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Jian Gao, Yun Gao, Fang-Wei Fu. 2014-02-27. On Linear Codes over $\mathbb{Z}_4+v\mathbb{Z}_4$. https://arxiv.org/abs/1402.6771

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