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Equitable [[2, 10], [6, 6]]-partitions of the 12-cube.
- Source :
- Cryptography & Communications; Sep2024, Vol. 16 Issue 5, p975-996, 22p
- Publication Year :
- 2024
-
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). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 19362447
- Volume :
- 16
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Cryptography & Communications
- Publication Type :
- Academic Journal
- Accession number :
- 179258893
- Full Text :
- https://doi.org/10.1007/s12095-024-00716-z