TY - JOUR
T1 - Characterization and classification of optimal LCD codes
AU - Araya, Makoto
AU - Harada, Masaaki
AU - Saito, Ken
N1 - Funding Information:
The authors would like to thank Tatsuya Maruta for his useful comments. This work was supported by JSPS KAKENHI Grant Number 19H01802.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.
PY - 2021/4
Y1 - 2021/4
N2 - Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over Fq having large minimum weights for q∈ { 2 , 3 }. Using the characterization, for arbitrary n, we determine the largest minimum weights among LCD [n, k] codes over Fq, where (q, k) ∈ { (2 , 4) , (3 , 2) , (3 , 3) }. Moreover, for arbitrary n, we give a complete classification of optimal LCD [n, k] codes over Fq, where (q, k) ∈ { (2 , 3) , (2 , 4) , (3 , 2) , (3 , 3) }.
AB - Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over Fq having large minimum weights for q∈ { 2 , 3 }. Using the characterization, for arbitrary n, we determine the largest minimum weights among LCD [n, k] codes over Fq, where (q, k) ∈ { (2 , 4) , (3 , 2) , (3 , 3) }. Moreover, for arbitrary n, we give a complete classification of optimal LCD [n, k] codes over Fq, where (q, k) ∈ { (2 , 3) , (2 , 4) , (3 , 2) , (3 , 3) }.
KW - Binary code
KW - Griesmer bound
KW - Linear complementary dual code
KW - Simple code
KW - Ternary code
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U2 - 10.1007/s10623-020-00834-8
DO - 10.1007/s10623-020-00834-8
M3 - Article
AN - SCOPUS:85099558796
SN - 0925-1022
VL - 89
SP - 617
EP - 640
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 4
ER -