Additive semisimple multivariable codes over $${\mathbb{F}_4}$$

Abstract

The structure of additive multivariable codes over $${\mathbb{F}_4}$$ (the Galois field with 4 elements) is presented. The semisimple case (i.e., when the defining polynomials of the code have no repeated roots) is specifically addressed. These codes extend in a natural way the abelian codes, of which additive cyclic codes of odd length are a particular case. Duality of these codes is also studied.