Códigos cíclicos e sua distribuição de pesos

Abstract

The objective of this work is, study minimal cyclic codes viewed as ideals of a group algebra FqG, where Fq is a finite field q elements and G a finite cyclic group of order n. Imposing conditions at n and q, we determined explicit expressions for the primitive idempotents of this algebra. To do this, we determined which and how many irreducible factors had the polynomial xn - 1 over the field Fq. In particular, ourconditions ensure that every factors are irreducible binomials or trinomials. Finally, we calculated the weight distribution of these codes using the same techniques found in [15].