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arXiv · 1704.03519

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

A. Melakhessou·K. Guenda·T. A. Gulliver·M. Shi·P. Solé
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Abstract

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

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A. Melakhessou, K. Guenda, T. A. Gulliver, M. Shi, P. Solé. 2017-04-11. On Codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$. https://arxiv.org/abs/1704.03519

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