PreprintCC BY 4.0arXiv
New binary optimal LCD codes using heuristic embedding
Abstract
In this paper, we investigate the construction of binary optimal LCD codes through short LCD embeddings. For this purpose, we design heuristic frameworks based on a greedy algorithm. We explore the search spaces of LCD embeddings using the fact that an invertible matrix together with an arbitrary matrix yields an LCD embedding. We therefore use elementary row operations on the invertible block and single entry-flips on the arbitrary block as local moves in a greedy algorithm. Using this method, we have found $14$ optimal new LCD codes with dimensions 7 and 8 for lengths from 55 to 201.
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BibTeX
@misc{lim2026binary,
title = {{New binary optimal LCD codes using heuristic embedding}},
author = {Haeun Lim and Junmin An and Jon-Lark Kim},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02096},
eprint = {2609.02096},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02096},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - New binary optimal LCD codes using heuristic embedding
AU - Haeun Lim
AU - Junmin An
AU - Jon-Lark Kim
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02096
UR - https://arxiv.org/abs/2609.02096
AB - In this paper, we investigate the construction of binary optimal LCD codes through short LCD embeddings. For this purpose, we design heuristic frameworks based on a greedy algorithm. We explore the search spaces of LCD embeddings using the fact that an invertible matrix together with an arbitrary matrix yields an LCD embedding. We therefore use elementary row operations on the invertible block and single entry-flips on the arbitrary block as local moves in a greedy algorithm. Using this method, we have found $14$ optimal new LCD codes with dimensions 7 and 8 for lengths from 55 to 201.
ER -