Open AccessGood Linear Codes from Quadratic Residue Codes over a Finite Non‐Chain Ring
Author(s) -
Gao Jian,
Ma Fanghui
Publication year - 2017
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.2017.05.001
Subject(s) - quadratic residue , residue (chemistry) , ring (chemistry) , mathematics , chain (unit) , quadratic equation , discrete mathematics , chemistry , physics , geometry , biochemistry , organic chemistry , astronomy
This paper is devoted to the study of quadratics residue codes and their extended codes over a finite non‐chain ring. A class of Gray maps preserving the self‐duality from the ring to the finite field are introduced. Some structural properties of quadratic residue codes and their extended codes are given. As an interesting application of these families of codes, some good linear codes are obtained by a special Gray map.