Section: New Results

Quasi-cyclic codes

M. Barbier, Christophe Chabot and G. Quintin exhibited a bijective correspondence between the $\ell$-quasi-cyclic codes over ${𝔽}_q$ of length $m\ell$ and the set of ideals of $M_{\ell }\left({𝔽}_q\right)\left[X\right]/(X^m-1)$ [29] . They proposed also two new classes called the quasi-BCH and quasi-evaluation codes. For the first one, they introduced a unambiguous decoding algorithm, and thanks to the second one they designed 49 new codes over ${𝔽}_4$ which have a bigger minimum distance than previously known codes.