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Four New Single-Error-Correcting Binary Codes
Abstract
We construct a $(16, 3072, 3)$-code, a $(17,6144,3)$-code, an $(18,12288,3)$-code and a $(19,24576,3)$-code. Consequently, we get four new lower bounds: A(16,3) ≥ 3072, A(17,3) ≥ 6144, A(18,3) ≥ 12288 and A(19,3) ≥ 24576. Each of the codes consists of a union of cosets of a linear code. The constructions are the result of a computer search executing a tabu search algorithm.
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BibTeX
@misc{milshtein2026four,
title = {{Four New Single-Error-Correcting Binary Codes}},
author = {Moshe Milshtein},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23626},
eprint = {2610.23626},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23626},
}
RIS
TY - UNPB
TI - Four New Single-Error-Correcting Binary Codes
AU - Moshe Milshtein
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23626
UR - https://arxiv.org/abs/2610.23626
AB - We construct a $(16, 3072, 3)$-code, a $(17,6144,3)$-code, an $(18,12288,3)$-code and a $(19,24576,3)$-code. Consequently, we get four new lower bounds: A(16,3) ≥ 3072, A(17,3) ≥ 6144, A(18,3) ≥ 12288 and A(19,3) ≥ 24576. Each of the codes consists of a union of cosets of a linear code. The constructions are the result of a computer search executing a tabu search algorithm.
ER -