The structure of one weight linear and cyclic codes over Zr 2 × (Z2 + uZ2)s

Abstract

Inspired by the Z2Z4-additive codes, linear codes over Zr2 × (Z2 + uZ2)s havebeen introduced by Aydogdu et al. more recently. Although these familyof codes are similar to each other, linear codes over Zr2 × (Z2 + uZ2)s havesome advantages compared to Z2Z4-additive codes. A code is called constantweight (one weight) if all the nonzero codewords have the same weight. It iswell known that constant weight or one weight codes have many importantapplications. In this paper, we study the structure of one weight Z2Z2[u]-linear and cyclic codes. We classify one weight Z2Z2[u]-cyclic codes and alsogive some illustrative examples.