Equitable [[2, 10], [6, 6]]-partitions of the 12-cube

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 classificati...

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Bibliographic Details
Published inCryptography and communications Vol. 16; no. 5; pp. 975 - 996
Main Author Krotov, Denis S.
Format Journal Article
LanguageEnglish
Published New York Springer US 2024
Springer Nature B.V
Subjects
Boolean functions
Circuits
Classification
Coding and Information Theory
Communications Engineering
Computer Science
Correlation
Data Structures and Information Theory
Equivalence
Information and Communication
Mathematics of Computing
Networks
Orthogonal arrays
Quotients
Equitable partitions
94D10
Perfect colorings
Correlation-immune boolean functions
05B15
Intriguing sets
Orthogonal arrays
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Summary: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).
ISSN:1936-2447
1936-2455
DOI:10.1007/s12095-024-00716-z