The Structure of Z_2[u]Z_2[u, v]-additive Codes

TL;DR

This paper explores the algebraic structure of Z_2[u]Z_2[u, v]-additive codes, establishing their properties, Gray map, and generator matrices, and analyzing cyclic and constacyclic codes within this framework.

Contribution

It introduces a Gray map and characterizes generator and parity check matrices for Z_2[u]Z_2[u, v]-additive codes, including cyclic and constacyclic subclasses.

Findings

Defined a Gray map from Z_2[u]Z_2[u, v] to binary space.

Characterized generator and parity check matrices for these codes.

Analyzed the structure of cyclic and constacyclic codes.

Abstract

In this paper, we study the algebraic structure of Z_2[u]Z_2[u, v]-additive codes which are Z_2[u, v]-submodules where u^2 = v^2 = 0 and uv = vu. In particular, we determine a Gray map from Z_2[u]Z_2 [u, v] to Z_2^{2{\alpha}+8\b{eta}} and study generator and parity check matrices for these codes. Further we study the structure of Z_2[u]Z_2[u, v]-additive cyclic codes and constacyclic codes.