The seminar on

MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE

organized by

the Department of Mathematical Foundations of Informatics at IMI – BAS and

the Faculty of Mathematics and Informatics of Veliko Tarnovo University (VTU),

would like to invite you to the next meeting on January 8, 2025 at 5:00 p.m. in room 401 of building 4 of VTU.

Prof. Ferruh Özbudak

Sabancı University
Faculty of Engineering and Natural Sciences,
İstanbul – Turkiye

will deliver a talk on:

Generalizing the Bierbrauer—Friedman bound to mixed-level orthogonal arrays

(joint work with Denis Krotov and Vladimir Potapov)

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. 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.

Acknowledgment: The work of F.Ö. was supported by TÜBİTAK under Grant 223N065.

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