Steiner Systems over Mixed Alphabet and Related Designs
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915365493145600 |
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| author | Etzion, Tuvi |
| author_facet | Etzion, Tuvi |
| contents | A mixed Steiner system MS$(t,k,Q)$ is a set (code) $C$ of words of weight $k$ over an alphabet $Q$, where not all coordinates of a word have the same alphabet size, each word of weight $t$, over $Q$, has distance $k-t$ from exactly one codeword of $C$, and the minimum distance of the code $2(k-t)+1$. Mixed Steiner systems are constructed from perfect mixed codes, resolvable designs, large set, orthogonal arrays, and a new type of pairs-triples design. Necessary conditions for the existence of mixed Steiner systems are presented and it is proved that there are no large sets of these Steiner systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23860 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Steiner Systems over Mixed Alphabet and Related Designs Etzion, Tuvi Combinatorics A mixed Steiner system MS$(t,k,Q)$ is a set (code) $C$ of words of weight $k$ over an alphabet $Q$, where not all coordinates of a word have the same alphabet size, each word of weight $t$, over $Q$, has distance $k-t$ from exactly one codeword of $C$, and the minimum distance of the code $2(k-t)+1$. Mixed Steiner systems are constructed from perfect mixed codes, resolvable designs, large set, orthogonal arrays, and a new type of pairs-triples design. Necessary conditions for the existence of mixed Steiner systems are presented and it is proved that there are no large sets of these Steiner systems. |
| title | Steiner Systems over Mixed Alphabet and Related Designs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.23860 |