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arXiv · 2411.16559

Generalizing the Bierbrauer-Friedman bound for orthogonal arrays

Denis S. Krotov·Ferruh Özbudak·Vladimir N. Potapov
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Abstract

We characterize mixed-level orthogonal arrays in 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. Keywords: orthogonal array, algebraic t-design, completely regular code, equitable partition, intriguing set, Hamming graph, Bierbrauer-Friedman bound, additive codes.

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Denis S. Krotov, Ferruh Özbudak, Vladimir N. Potapov. 2024-11-25. Generalizing the Bierbrauer-Friedman bound for orthogonal arrays. https://doi.org/10.1007/s10623-025-01711-y

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