Embedding Linear Codes into Optimal Self-Orthogonal Codes Based on Constraint-Preserving Genetic Algorithms
Abstract
We study the problem of finding shortest self-orthogonal embeddings of a given code which have the largest possible minimum distance by employing a constraint-preserving genetic algorithm. We show that the orthogonal group is generated by transvections corresponding to weight-four vectors. Using this result together with the fact that all shortest self-orthogonal embeddings can be obtained through the action of the orthogonal group, we construct a genetic algorithm in which each chromosome is represented by a sequence of weight-four vectors. Applying our algorithm to codes with dimensions 9≤ k≤ 15 and lengths 22≤ n≤ 256, we obtain 280 inequivalent optimal self-orthogonal codes. In particular, we obtain 34 codes with new parameters and 100 codes which are inequivalent to previously known codes with the same parameters.
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BibTeX
@misc{lim2026embedding,
title = {{Embedding Linear Codes into Optimal Self-Orthogonal Codes Based on Constraint-Preserving Genetic Algorithms}},
author = {Haeun Lim and Junmin An and Jon-Lark Kim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.02135},
eprint = {2609.02135},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02135},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Embedding Linear Codes into Optimal Self-Orthogonal Codes Based on Constraint-Preserving Genetic Algorithms
AU - Haeun Lim
AU - Junmin An
AU - Jon-Lark Kim
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2609.02135
UR - https://arxiv.org/abs/2609.02135
AB - We study the problem of finding shortest self-orthogonal embeddings of a given code which have the largest possible minimum distance by employing a constraint-preserving genetic algorithm. We show that the orthogonal group is generated by transvections corresponding to weight-four vectors. Using this result together with the fact that all shortest self-orthogonal embeddings can be obtained through the action of the orthogonal group, we construct a genetic algorithm in which each chromosome is represented by a sequence of weight-four vectors. Applying our algorithm to codes with dimensions 9≤ k≤ 15 and lengths 22≤ n≤ 256, we obtain 280 inequivalent optimal self-orthogonal codes. In particular, we obtain 34 codes with new parameters and 100 codes which are inequivalent to previously known codes with the same parameters.
ER -