Abstract: We characterize mixed-level orthogonal arrays it 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. This is joint work with Ferruh Ozbudak and Vladimir Potapov.

Cite: Krotov D.S.
Generalizing the Bierbrauer-Friedman bound to mixed-level orthogonal arrays
2024 年组合、编码与密码国际研讨会 2024 International Symposium on Combinatorics, Coding and Cryptography 27-29 Dec 2024