Equitable [[2, 10], [6, 6]]-partitions of the 12-cube Full article
| Journal |
Cryptography and Communications
ISSN: 1936-2447 , E-ISSN: 1936-2455 |
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| Output data | Year: 2024, Volume: 16, Pages: 975–996 Pages count : DOI: 10.1007/s12095-024-00716-z | ||
| Tags | Orthogonal arrays · Correlation-immune boolean functions · Equitable partitions · Perfect colorings · Intriguing sets | ||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Russian Science Foundation | 22-11-00266 |
| 2 | Russian Science Foundation | 18-11-00136 |
Abstract:
We describe the computer-aided classification of equitable partitions of the 12-cube with quotient matrix [[2, 10], [6, 6]], or, equivalently, simple orthogonal arrays OA(1536, 12, 2, 7), or order-7 correlation-immune Boolean functions in 12 arguments with 1536 ones (which completes the classification of unbalanced order-7 correlation-immune Boolean functions in 12 arguments and, as derived objects, unbalanced order-6 correlation-immune Boolean functions in 11 arguments). We find that there are 103 equivalence classes of the considered objects, and there are only two almost-OA(1536, 12, 2, 8) among them. Additionally, we find that there are 40 equivalence classes of pairs of disjoint simple OA(1536, 12, 2, 7) (equivalently, equitable partitions of the 12-cube with quotient matrix [[2, 6, 4], [6, 2, 4], [6, 6, 0]]) and discuss the existence of a non-simple OA(1536, 12, 2, 7).
Cite:
Krotov D.S.
Equitable [[2, 10], [6, 6]]-partitions of the 12-cube
Cryptography and Communications. 2024. V.16. P.975–996. DOI: 10.1007/s12095-024-00716-z WOS Scopus РИНЦ OpenAlex
Equitable [[2, 10], [6, 6]]-partitions of the 12-cube
Cryptography and Communications. 2024. V.16. P.975–996. DOI: 10.1007/s12095-024-00716-z WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jul 20, 2023 |
| Accepted: | Apr 17, 2024 |
| Published online: | Apr 26, 2024 |
| Published print: | Sep 18, 2024 |
Identifiers:
| Web of science: | WOS:001208647100001 |
| Scopus: | 2-s2.0-85191384767 |
| Elibrary: | 67079267 |
| OpenAlex: | W3110367038 |