Binary Images of Z2Z4-Additive Cyclic Codes

TL;DR

This paper investigates the structure of Z2Z4-additive cyclic codes and characterizes those with odd beta whose Gray images are linear binary codes, expanding understanding of their algebraic properties.

Contribution

It provides a complete classification of Z2Z4-additive cyclic codes with odd beta that have linear Gray images, a novel characterization in coding theory.

Findings

Identified all Z2Z4-additive cyclic codes with odd beta and linear Gray images.

Established conditions under which Gray images of these codes are linear.

Enhanced understanding of the algebraic structure of Z2Z4-additive cyclic codes.

Abstract

A Z2Z4-additive code C is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z_2 and the set of Z_4 coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. We study the binary images of Z2Z4-additive cyclic codes. We determine all Z2Z4-additive cyclic codes with odd beta whose Gray images are linear binary codes.