# The Structure of One Weight Linear and Cyclic Codes Over Z2^r x (Z2+uZ2)^s

## TL;DR

This paper investigates the structure and classification of one weight linear and cyclic codes over the ring Z2^r x (Z2+uZ2)^s, highlighting their advantages and providing illustrative examples.

## Contribution

It introduces a classification of one weight Z2Z2[u]-linear and cyclic codes, expanding understanding of their structure and properties.

## Key findings

- Classified one weight Z2Z2[u]-linear codes.
- Analyzed the structure of cyclic codes over the specified ring.
- Provided examples illustrating the code classifications.

## Abstract

Inspired by the Z2Z4-additive codes, linear codes over Z2^r x(Z2+uZ2)^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z2^r x(Z2+uZ2)^s have some advantages compared to Z2Z4-additive codes. A code is called constant weight(one weight) if all the codewords have the same weight. It is well known that constant weight or one weight codes have many important applications. In this paper, we study the structure of one weight Z2Z2[u]-linear and cyclic codes. We classify these type of one weight codes and also give some illustrative examples.