TY - JOUR
T1 - Linear complementary dual codes over rings
AU - Liu, Zihui
AU - Wang, Jinliang
N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - By using linear algebra over finite commutative rings, we will present some judging criterions for linear complementary dual (LCD) codes over rings, in particular, free LCD codes over finite commutative rings are described. By using free LCD codes over finite commutative rings and the Chinese Remainder Theorem, LCD codes over semi-simple rings are constructed and the equivalence of free codes and free LCD codes is given. In addition, all the possible LCD codes over chain rings are determined. We also generalize the judging criterion for cyclic LCD codes over finite fields to cyclic LCD codes over chain rings. Based on the above results and the Chinese Remainder Theorem, we also present results for LCD codes over principal ideal rings.
AB - By using linear algebra over finite commutative rings, we will present some judging criterions for linear complementary dual (LCD) codes over rings, in particular, free LCD codes over finite commutative rings are described. By using free LCD codes over finite commutative rings and the Chinese Remainder Theorem, LCD codes over semi-simple rings are constructed and the equivalence of free codes and free LCD codes is given. In addition, all the possible LCD codes over chain rings are determined. We also generalize the judging criterion for cyclic LCD codes over finite fields to cyclic LCD codes over chain rings. Based on the above results and the Chinese Remainder Theorem, we also present results for LCD codes over principal ideal rings.
KW - Chain rings
KW - Chinese Remainder Theorem
KW - Generating polynomial
KW - LCD codes
KW - Principal ideal rings
UR - http://www.scopus.com/inward/record.url?scp=85069682014&partnerID=8YFLogxK
U2 - 10.1007/s10623-019-00664-3
DO - 10.1007/s10623-019-00664-3
M3 - Article
AN - SCOPUS:85069682014
SN - 0925-1022
VL - 87
SP - 3077
EP - 3086
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 12
ER -