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Z2 (Z2+uZ2)(Z2+uZ2+u2Z2)-Additive Cyclic Codes
Engineering Mathematics
Volume 3, Issue 2, December 2019, Pages: 30-39
Received: Jun. 14, 2019; Accepted: Oct. 11, 2019; Published: Oct. 25, 2019
Volume 3, Issue 2, December 2019, Pages: 30-39
Received: Jun. 14, 2019; Accepted: Oct. 11, 2019; Published: Oct. 25, 2019
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Author
Zhihui Li, Department of Mathematics, School of Mathematics and Statistics, Shandong University of Technology, Zibo, China
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.
Keywords
Additive Codes, Cyclic Codes, Minimal Generating Set
To cite this article
Zhihui Li,
Z2 (Z2+uZ2)(Z2+uZ2+u2Z2)-Additive Cyclic Codes, Engineering Mathematics.
Vol. 3, No. 2,
2019, pp. 30-39.
doi: 10.11648/j.engmath.20190302.11
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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