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

A. Melakhessou; K. Guenda; M. Shi; P. Sol\'e; T. A. Gulliver

arxiv: 1704.03519 · v1 · pith:FUSILTNBnew · submitted 2017-04-11 · 💻 cs.IT · math.IT· math.RA

On Codes over mathbb{F}_(q)+vmathbb{F}_(q)+v²mathbb{F}_(q)

A. Melakhessou , K. Guenda , T. A. Gulliver , M. Shi , P. Sol\'e This is my paper

classification 💻 cs.IT math.ITmath.RA

keywords codesmathbbformallygiveself-dualboundscomplementaryconditions

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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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On Codes over mathbb{F}_(q)+vmathbb{F}_(q)+v²mathbb{F}_(q)

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