One weight $$\mathbb {Z}_2\mathbb {Z}_4$$ Z 2 Z 4 additive codes

Dougherty, Steven T.; Liu, Hongwei; Yu, Lei

doi:10.1007/s00200-015-0273-4

Cited by 11 publications

(1 citation statement)

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“…A Z 2 Z 4 -additive code C is defined to be a subgroup of [4], and recently this generalization has extended to Z p r Z p s -additive codes, for a prime p, by the same authors in [6]. Later, cyclic codes over Z α 2 × Z β 4 have been introduced in [1] in 2014 and more recently, in [13], one weight codes over such a mixed alphabet have been studied. A code C is said to be one weight code if all the nonzero codewords of a code have the same Hamming weight where the Hamming weight of an any codeword is defined as the number of its nonzero coordinates.…”

Section: Introductionmentioning

confidence: 99%

The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s

Aydoğdu

2017

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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Inspired by the Z2Z4-additive codes, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^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.

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Section: Introductionmentioning

confidence: 99%