Z2 (Z2+uZ2)(Z2+uZ2+u2Z2)-Additive Cyclic Codes
Issue:
Volume 3, Issue 2, December 2019
Pages:
30-39
Received:
14 June 2019
Accepted:
11 October 2019
Published:
25 October 2019
Abstract: In this paper, we introduce the algebraic structure of Z2 (Z2+uZ2) (Z2+uZ2+u2Z2) -additive codes and Z2 (Z2+uZ2) (Z2+uZ2+u2Z2) -additive cyclic codes. Compared to the Z2Z4Z8-additive codes, the Gray image of any Z2 (Z2+uZ2) (Z2+uZ2+u2Z2) -linear code will always be a linear binary code. Therefore, we consider the Z2 (Z2+uZ2) (Z2+uZ2+u2Z2) -additive cyclic codes as a (Z2+uZ2+u2Z2) [x] -submodule of Z2α×(Z2+uZ2)β×(Z2+uZ2+u2Z2)θ. We give the definition of Z2 (Z2+uZ2) (Z2+uZ2+u2Z2) -additive codes with generator matrices and parity-check matrices. Furthermore, we give the fundamental result on considering their additive cyclic codes with generator polynomials and spanning sets.
Abstract: In this paper, we introduce the algebraic structure of Z2 (Z2+uZ2) (Z2+uZ2+u2Z2) -additive codes and Z2 (Z2+uZ2) (Z2+uZ2+u2Z2) -additive cyclic codes. Compared to the Z2Z4Z8-additive codes, the Gray image of any Z2 (Z2+uZ2) (Z2+uZ2+u2Z2) -linear code will always be a linear binary code. Therefore, we consider the Z2 (Z2+uZ2) (Z2+uZ2+u2Z2) -additive...
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