TY - JOUR
T1 - A method for constructing quaternary Hermitian self-dual codes and an application to quantum codes
AU - Harada, Masaaki
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/10
Y1 - 2024/10
N2 - We introduce quaternary modified four μ-circulant codes as a modification of four circulant codes. We give basic properties of quaternary modified four μ-circulant Hermitian self-dual codes. We also construct quaternary modified four μ-circulant Hermitian self-dual codes having large minimum weights. Two quaternary Hermitian self-dual [56, 28, 16] codes are constructed for the first time. These codes improve the previously known lower bound on the largest minimum weight among all quaternary (linear) [56, 28] codes. In addition, these codes imply the existence of a quantum [[56, 0, 16]] code.
AB - We introduce quaternary modified four μ-circulant codes as a modification of four circulant codes. We give basic properties of quaternary modified four μ-circulant Hermitian self-dual codes. We also construct quaternary modified four μ-circulant Hermitian self-dual codes having large minimum weights. Two quaternary Hermitian self-dual [56, 28, 16] codes are constructed for the first time. These codes improve the previously known lower bound on the largest minimum weight among all quaternary (linear) [56, 28] codes. In addition, these codes imply the existence of a quantum [[56, 0, 16]] code.
KW - 94B05
KW - Hermitian self-dual code
KW - Quaternary code
KW - Self-dual code
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U2 - 10.1007/s10623-024-01421-x
DO - 10.1007/s10623-024-01421-x
M3 - Article
AN - SCOPUS:85193727058
SN - 0925-1022
VL - 92
SP - 2927
EP - 2948
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 10
ER -