Construction of Butson matrices using Fourier matrices as input
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913803324620800 |
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| author | Adda, Farouk |
| author_facet | Adda, Farouk |
| contents | Butson matrices are square orthogonal matrices, denoted by $BH(m,n)$, whose entries are the complex $m$th roots of unity and satisfy the condition\\ $BH(m,n)\cdot{BH(m,n)}^*=nI_n$, where ${BH(m,n)}^*$ is the conjugate transpose of $BH(m,n)$ and $I_n$ is the identity matrix. In this work, we propose constructions for $BH(m,(n-1)n)$ then $BH(m,(\frac{n}{2}-1)n)$, when $n$ and $m$ are even numbers, using the existing $BH(m,n)$. For each case, we provide two construction methods: one uses a single input Butson matrix, and another uses two input Butson matrices. Moreover, we present some results about the construction of Hadamard matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction of Butson matrices using Fourier matrices as input Adda, Farouk Combinatorics 15B20 (Primary), 05C31 (Secondary) Butson matrices are square orthogonal matrices, denoted by $BH(m,n)$, whose entries are the complex $m$th roots of unity and satisfy the condition\\ $BH(m,n)\cdot{BH(m,n)}^*=nI_n$, where ${BH(m,n)}^*$ is the conjugate transpose of $BH(m,n)$ and $I_n$ is the identity matrix. In this work, we propose constructions for $BH(m,(n-1)n)$ then $BH(m,(\frac{n}{2}-1)n)$, when $n$ and $m$ are even numbers, using the existing $BH(m,n)$. For each case, we provide two construction methods: one uses a single input Butson matrix, and another uses two input Butson matrices. Moreover, we present some results about the construction of Hadamard matrices. |
| title | Construction of Butson matrices using Fourier matrices as input |
| topic | Combinatorics 15B20 (Primary), 05C31 (Secondary) |
| url | https://arxiv.org/abs/2504.15980 |