Codes Cycliques divisibles sur un Corps de Galois

Abstract

This work is devoted to the study of cyclic codes on a Galois field and the characterisation of the class of those having code words with a common divisor greater than one. We use the McEliece theorem to proove that a non degenerated binary code C is a divisible code if and only if 1 is a non zero of C. We also proove that if a binary non degenerated cyclic code is divisible, then its orthogonal is also divisible if and only if it is degenerated. For the general case were p is a prime, we give a necessary condition for a non degenarated cyclic code over Fp to be divisible.