Number theory days

Skew Generalized Quasi-Cyclic Codes

25 juin 2014, 11:45

1h

Salle de réunions (Université Lille 1)

Algèbre non commutative Algèbre non commutative

Orateur

Patrick Solé (Telecom ParisTech)

Description

In this article we introduce skew generalized quasi-cyclic codes over finite field $F$ with Galois automorphism $\theta$. This is a generalization of quasi-cyclic codes and skew polynomial codes. These codes have an added advantage over quasi-cyclic codes, since the length of the code $C$ need not be a multiple of the index of $C$. After a brief description of the skew polynomial ring $F[x;\theta ]$, it is shown that a skew generalized quasi-cyclic code $C$ is a left submodule of $R_1\times R_2\times \cdots R_l$, where $R_i=F[x;\theta ]/(x^{m_i}-1),\left|⟨\theta ⟩\right|=m$ and $m|m_i$ for all $i=1,\dots ,l$. This method provides a direct construction of many codes with best known parameters over $GF(4)$. Joint work with T. Abualrub, P. Seneviratne