Year: 2014
Type: preprint
Abstract: A ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive code ${\cal C}\subseteq{\mathbb{Z}}_2^α\times{\mathbb{Z}}_4^β$ 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 $\mathbb{Z}_2[x]/(x^α-1)\times\mathbb{Z}_4[x]/(x^β-1)$. The parameters of a ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive cyclic code are stated in terms of the degrees of the generator polynomials of the code. The generator polynomials of the dual code of a ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive cyclic code are determined in terms of the generator polynomials of the code ${\cal C}$.
Source: arXiv (Cornell University)
Institution: Universitat Autònoma de Barcelona
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2118912475