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On Codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$ (1704.03519v1)
Published 11 Apr 2017 in cs.IT, math.IT, and math.RA
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 $R$.