Open AccessOne and Two‐Weight ℤ 2 R 2 Additive Codes
Author(s) -
Tiantian Li,
Minjia Shi,
Bo Lin,
Wenting Wu
Publication year - 2021
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.2020.10.011
Subject(s) - generalization , mathematics , code (set theory) , identity (music) , minimum weight , discrete mathematics , algebra over a field , combinatorics , computer science , pure mathematics , physics , programming language , mathematical analysis , set (abstract data type) , acoustics
This paper is devoted to the construction of one and two‐weightZ 2 R 2additive codes, whereR 2 = F 2 [ v ] / 〈 v 4 〉. It is a generalization towards another direction ofZ 2 Z 4codes (S.T. Dougherty, H.W. Liu and L. Yu, “One weightZ 2 Z 4additive codes”, Applicable Algebra in Engineering, Communication and Computing , Vol.27, No.2, pp.123‐138, 2016). A MacWilliams identity which connects the weight enumerator of an additive code overZ 2 R 2and its dual is established. Several construction methods of one‐weight and two‐weight additive codes overZ 2 R 2are presented. Several examples are presented to illustrate our main results and some open problems are also proposed.