Generalizing the Bierbrauer-Friedman bound for orthogonal arrays
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915587162112000 |
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| author | Krotov, Denis S. Özbudak, Ferruh Potapov, Vladimir N. |
| author_facet | Krotov, Denis S. Özbudak, Ferruh Potapov, Vladimir N. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_16559 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalizing the Bierbrauer-Friedman bound for orthogonal arrays Krotov, Denis S. Özbudak, Ferruh Potapov, Vladimir N. Combinatorics Discrete Mathematics 05B15, 51E23 (Primary), 05E30, 94B05 (Secondary) 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. |
| title | Generalizing the Bierbrauer-Friedman bound for orthogonal arrays |
| topic | Combinatorics Discrete Mathematics 05B15, 51E23 (Primary), 05E30, 94B05 (Secondary) |
| url | https://arxiv.org/abs/2411.16559 |