TY - JOUR
T1 - On the minimum weights of binary LCD codes and ternary LCD codes
AU - Araya, Makoto
AU - Harada, Masaaki
AU - Saito, Ken
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Number 19H01802 . The authors would also like to thank the anonymous referees for helpful comments.
Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/12
Y1 - 2021/12
N2 - Linear complementary dual (LCD) codes are linear codes that intersect with their dual codes trivially. We study the largest minimum weight d2(n,k) among all binary LCD [n,k] codes and the largest minimum weight d3(n,k) among all ternary LCD [n,k] codes. The largest minimum weights d2(n,5) and d3(n,4) are partially determined. We also determine the largest minimum weights d2(n,n−5), d3(n,n−i) for i∈{2,3,4}, and d3(n,k) for n∈{11,12,…,19}.
AB - Linear complementary dual (LCD) codes are linear codes that intersect with their dual codes trivially. We study the largest minimum weight d2(n,k) among all binary LCD [n,k] codes and the largest minimum weight d3(n,k) among all ternary LCD [n,k] codes. The largest minimum weights d2(n,5) and d3(n,4) are partially determined. We also determine the largest minimum weights d2(n,n−5), d3(n,n−i) for i∈{2,3,4}, and d3(n,k) for n∈{11,12,…,19}.
KW - Binary code
KW - Linear complementary dual code
KW - Minimum weight
KW - Ternary code
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U2 - 10.1016/j.ffa.2021.101925
DO - 10.1016/j.ffa.2021.101925
M3 - Article
AN - SCOPUS:85115071069
SN - 1071-5797
VL - 76
JO - Finite Fields and Their Applications
JF - Finite Fields and Their Applications
M1 - 101925
ER -