Seminar
Z2Z4-additive cyclic codes, Roger Ten-Valls, Universitat Autonoma de Barcelona, Mon, 27 March, 2017, 10:00 a.m. C-356
Abstract
A ${mathbb{Z}}_2{mathbb{Z}}_4$-additive code ${cal C}subseteq{mathbb{Z}}_2^alpha imes{mathbb{Z}}_4^eta$ is called cyclic if the set of coordinates can be partitioned into two subsets, the set of ${mathbb{Z}}_2$ and the set of ${mathbb{Z}}_4$ coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. These codes can be identified as submodules of the $mathbb{Z}_4[x]$-module $mathbb{Z}_2[x]/(x^alpha-1) imesmathbb{Z}_4[x]/(x^eta-1)$. In this talk, we give basic results of ${mathbb{Z}}_2{mathbb{Z}}_4$-additive codes in order to introduce the subfamily of cyclic codes. We present the algebraic structure and the generator polynomials of ${mathbb{Z}}_2{mathbb{Z}}_4$-additive cyclic codes. Also, we discuss the concept of duality defining a proper inner product for polynomials and determining the generator polynomials of the dual code of a ${mathbb{Z}}_2{mathbb{Z}}_4$-additive cyclic code in terms of the generator polynomials of the code.