Binary Codes From Subset Inclusion Matrices Full article
| Journal |
Journal of Combinatorial Designs
ISSN: 1063-8539 |
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| Output data | Year: 2025, DOI: 10.1002/jcd.22012 | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
In this paper, we study the minimum distances of binary linear codes with parity check matrices formed from subset inclusion matrices Wt,n,k, representing t-element subsets versus k-element subsets of an n-element set. We provide both lower and upper bounds on the minimum distances of these codes and determine the exact values for any t ≤ 3 and sufficiently large n. Our study combines design and integer linear programming techniques. The codes we consider are connected to locally recoverable codes, LDPC codes and combinatorial designs. Furthermore, we construct quasi-cyclic LDPC codes from inclusion matrices that exhibit performance comparable to or slightly better than MacKay-type codes when evaluated using bit flipping and min-sum algorithms.
Cite:
Marin A.D.
, Mogilnykh I.Y.
Binary Codes From Subset Inclusion Matrices
Journal of Combinatorial Designs. 2025. DOI: 10.1002/jcd.22012 WOS Scopus OpenAlex
Binary Codes From Subset Inclusion Matrices
Journal of Combinatorial Designs. 2025. DOI: 10.1002/jcd.22012 WOS Scopus OpenAlex
Dates:
| Published online: | Oct 12, 2025 |
Identifiers:
| Web of science: | WOS:001590939400001 |
| Scopus: | 2-s2.0-105018685141 |
| OpenAlex: | W4415093860 |
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