Quasi-cyclic codes as codes over rings of matrices

Pierre-Louis Cayrel (1) , Christophe Chabot , Abdelkader Necer (2)

1 CASED - Center for Advanced Security Research Darmstadt [Darmstadt]
2 DMI

Quasi cyclic codes over a nite eld are viewed as cyclic codes over a non commutative ring of matrices over a nite eld. This point of view permits to generalize some known results about linear recurring sequences and to propose a new construction of some quasi cyclic codes and self dual codes.

Domaines: Mathématiques [math]

Pierre-Louis Cayrel, Christophe Chabot, Abdelkader Necer. Quasi-cyclic codes as codes over rings of matrices. Finite Fields and Their Applications, 2010, 16 (2), pp.100-115. ⟨10.1016/j.ffa.2010.01.001⟩. ⟨hal-00637617⟩