PreprintCC BY 4.0arXiv
Classification of binary, ternary and quaternary Hermitian LCD codes
Abstract
We extend the complete classifications of linear complementary dual (LCD) codes from length 15 to length 19 in the binary case, from length 10 to length 15 in the ternary case and from length 12 to length 13 in the quaternary Hermitian case. The classification rests on a reduction of the monomial equivalence of LCD codes to graph isomorphism on the coordinates, combined with canonical augmentation.
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BibTeX
@misc{ishizuka2026classification,
title = {{Classification of binary, ternary and quaternary Hermitian LCD codes}},
author = {Keita Ishizuka},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30561},
eprint = {2610.30561},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30561},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classification of binary, ternary and quaternary Hermitian LCD codes
AU - Keita Ishizuka
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30561
UR - https://arxiv.org/abs/2610.30561
AB - We extend the complete classifications of linear complementary dual (LCD) codes from length 15 to length 19 in the binary case, from length 10 to length 15 in the ternary case and from length 12 to length 13 in the quaternary Hermitian case. The classification rests on a reduction of the monomial equivalence of LCD codes to graph isomorphism on the coordinates, combined with canonical augmentation.
ER -