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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2403.16284 |
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| _version_ | 1866929287392657408 |
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| author | Huczynska, Sophie Hume, Sophie |
| author_facet | Huczynska, Sophie Hume, Sophie |
| contents | Classical strong external difference families (SEDFs) are much-studied combinatorial structures motivated by information security applications; it is conjectured that only one classical abelian SEDF exists with more than two sets. Recently, non-disjoint SEDFs were introduced; it was shown that families of these exist with arbitrarily many sets. We present constructions for both classical and non-disjoint SEDFs, which encompass all known non-cyclotomic examples for either type (plus many new examples) using a sequence-based framework. Moreover, we introduce a range of new external difference structures (allowing set-sizes to vary, and sets to be replaced by multisets) in both the classical and non-disjoint case, and show how these may be applied to various communications applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16284 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New results on non-disjoint and classical strong external difference families Huczynska, Sophie Hume, Sophie Combinatorics 05B10 (Primary) 94A60, 94B60 (Secondary) Classical strong external difference families (SEDFs) are much-studied combinatorial structures motivated by information security applications; it is conjectured that only one classical abelian SEDF exists with more than two sets. Recently, non-disjoint SEDFs were introduced; it was shown that families of these exist with arbitrarily many sets. We present constructions for both classical and non-disjoint SEDFs, which encompass all known non-cyclotomic examples for either type (plus many new examples) using a sequence-based framework. Moreover, we introduce a range of new external difference structures (allowing set-sizes to vary, and sets to be replaced by multisets) in both the classical and non-disjoint case, and show how these may be applied to various communications applications. |
| title | New results on non-disjoint and classical strong external difference families |
| topic | Combinatorics 05B10 (Primary) 94A60, 94B60 (Secondary) |
| url | https://arxiv.org/abs/2403.16284 |