TY - JOUR
T1 - Quaternary Hermitian Linear Complementary Dual Codes
AU - Araya, Makoto
AU - Harada, Masaaki
AU - Saito, Ken
N1 - Funding Information:
Manuscript received April 16, 2019; revised September 2, 2019; accepted October 8, 2019. Date of publication October 30, 2019; date of current version April 21, 2020. This work was supported by JSPS KAKENHI Grant Number 15H03633.
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2020/5
Y1 - 2020/5
N2 - The largest minimum weights among quaternary Hermitian linear complementary dual codes are known for dimension 2. In this paper, we give some conditions on the nonexistence of quaternary Hermitian linear complementary dual codes with large minimum weights. As a consequence, we completely determine the largest minimum weights for dimension 3, by using a classification of some quaternary codes. In addition, for a positive integer s, an entanglement-assisted quantum error-correcting $[[21{s}+5,3,16{s}+3;21{s}+2]]$ code with maximal entanglement is constructed for the first time from a quaternary Hermitian linear complementary dual [26, 3, 19] code.
AB - The largest minimum weights among quaternary Hermitian linear complementary dual codes are known for dimension 2. In this paper, we give some conditions on the nonexistence of quaternary Hermitian linear complementary dual codes with large minimum weights. As a consequence, we completely determine the largest minimum weights for dimension 3, by using a classification of some quaternary codes. In addition, for a positive integer s, an entanglement-assisted quantum error-correcting $[[21{s}+5,3,16{s}+3;21{s}+2]]$ code with maximal entanglement is constructed for the first time from a quaternary Hermitian linear complementary dual [26, 3, 19] code.
KW - Griesmer bound
KW - Hermitian linear complementary dual code
KW - Quaternary code
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U2 - 10.1109/TIT.2019.2949040
DO - 10.1109/TIT.2019.2949040
M3 - Article
AN - SCOPUS:85084128062
VL - 66
SP - 2751
EP - 2759
JO - IRE Professional Group on Information Theory
JF - IRE Professional Group on Information Theory
SN - 0018-9448
IS - 5
M1 - 8887244
ER -