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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2511.11230 |
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| _version_ | 1866918202073677824 |
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| author | Czifra, Domonkos Matolcsi, Máté Szöllősi, Ferenc |
| author_facet | Czifra, Domonkos Matolcsi, Máté Szöllősi, Ferenc |
| contents | Based on the concept of positive definite functions on finite groups, we present a new necessary condition for the existence of Butson Hadamard matrices $BH(n,q)$. We use this condition to prove some nonexistence results for a sequence of values of $(n,q)$, and also to facilitate a computer search and discover a matrix $BH(18,14)$. Furthermore, we use cyclotomic cosets to construct matrices $BH(34,10)$, $BH(62,6)$, $BH(82,6)$, and $BH(146,6)$ for the first time. These matrices have a $2$-circulant structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11230 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A nonexistence criterion and new constructions for Butson Hadamard matrices Czifra, Domonkos Matolcsi, Máté Szöllősi, Ferenc Combinatorics 05B20 Based on the concept of positive definite functions on finite groups, we present a new necessary condition for the existence of Butson Hadamard matrices $BH(n,q)$. We use this condition to prove some nonexistence results for a sequence of values of $(n,q)$, and also to facilitate a computer search and discover a matrix $BH(18,14)$. Furthermore, we use cyclotomic cosets to construct matrices $BH(34,10)$, $BH(62,6)$, $BH(82,6)$, and $BH(146,6)$ for the first time. These matrices have a $2$-circulant structure. |
| title | A nonexistence criterion and new constructions for Butson Hadamard matrices |
| topic | Combinatorics 05B20 |
| url | https://arxiv.org/abs/2511.11230 |