Generalizing the Bierbrauer–Friedman bound for orthogonal arrays Full article
| Journal |
Designs, Codes and Cryptography
ISSN: 0925-1022 , E-ISSN: 1573-7586 |
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| Output data | Year: 2025, DOI: 10.1007/s10623-025-01711-y | ||||||
| Tags | Orthogonal array, Algebraic t-design, Completely regular code, Equitable partition, Intriguing set, Hamming graph, Bierbrauer–Friedman bound, Additive codes | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
We characterize mixed-level orthogonal arrays in terms of algebraic designs in a special multigraph. We prove a mixed-level analog of the Bierbrauer–Friedman (BF) bound for pure-level orthogonal arrays and show that arrays attaining it are radius-1 completely regular codes (equivalently, intriguing sets, equitable 2-partitions, perfect 2-colorings) in the corresponding multigraph. For the case when the numbers of levels are powers of the same prime number, we characterize, in terms of multispreads, additive mixed-level orthogonal arrays attaining the BF bound. For pure-level orthogonal arrays, we consider versions of the BF bound obtained by replacing the Hamming graph by its polynomial generalization and show that in some cases this gives a new bound.
Cite:
Krotov D.S.
, Özbudak F.
, Potapov V.N.
Generalizing the Bierbrauer–Friedman bound for orthogonal arrays
Designs, Codes and Cryptography. 2025. DOI: 10.1007/s10623-025-01711-y WOS Scopus OpenAlex
Generalizing the Bierbrauer–Friedman bound for orthogonal arrays
Designs, Codes and Cryptography. 2025. DOI: 10.1007/s10623-025-01711-y WOS Scopus OpenAlex
Dates:
| Submitted: | Dec 31, 2024 |
| Accepted: | Aug 2, 2025 |
| Published online: | Aug 13, 2025 |
Identifiers:
| Web of science: | WOS:001552613400001 |
| Scopus: | 2-s2.0-105013284177 |
| OpenAlex: | W4413128282 |
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