Open AccessAsymptotically Good Additive Cyclic Codes
Author(s) -
Yao Ting,
Zhu Shixin,
Kai Xiaoshan
Publication year - 2020
Publication title -
chinese journal of electronics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 25
eISSN - 2075-5597
pISSN - 1022-4653
DOI - 10.1049/cje.2020.05.013
Subject(s) - computer science , mathematics
Z p Z p s ‐additive cyclic codes have been proved to be asymptotically good by Yao and Zhu. For binary Hamming scheme, we introduce a type of Z 2 ( Z 2 + u Z 2 )‐additive cyclic codes generated by pairs of polynomials. Let R be the chain ring Z 2 + uZ 2 , where u 2 = 0. The asymptotic rates and relative distances of this class of codes are presented by establishing the relationship between the random Z 2 R ‐additive cyclic code and random binary quasi‐cyclic code of index 2. We show that Z 2 R ‐additive cyclic codes are asymptotically good.