Constructions of Butson Hadamard matrices invariant under Abelian p-groups
Let a and h be positive integers and let p be a prime. Let q1,…,qt be the distinct prime divisors of h and write Q(h)={∑i=1tciqi:ci∈Z,ci≥0}. We provide constructions of group invariant Butson Hadamard matrices BH(G,h) in the following cases. 1. G=(Zp)2a and at least one of the following conditions i...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/159805 |
| _version_ | 1811682906564722688 |
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| author | Schmidt, Bernhard Wong, Dai Quan Xiang, Qing |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Schmidt, Bernhard Wong, Dai Quan Xiang, Qing |
| author_sort | Schmidt, Bernhard |
| collection | NTU |
| description | Let a and h be positive integers and let p be a prime. Let q1,…,qt be the distinct prime divisors of h and write Q(h)={∑i=1tciqi:ci∈Z,ci≥0}. We provide constructions of group invariant Butson Hadamard matrices BH(G,h) in the following cases. 1. G=(Zp)2a and at least one of the following conditions is satisfied. • pa∈Q(h), • pa+2∈Q(h) and h is even, • pa+1=(q1−1)(q2−1) where q1 and q2 are distinct prime divisors of h. 2. G=Zpa×Zpa and p−1,p∈Q(h). 3. G=(Zp2)a and pb∈Q(h) for some divisor b of a with 1≤b<a. 4. G=P×Zpa where P is any abelian group of order pa and p∈Q(h). |
| first_indexed | 2024-10-01T04:04:17Z |
| format | Journal Article |
| id | ntu-10356/159805 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:04:17Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1598052022-07-04T01:46:29Z Constructions of Butson Hadamard matrices invariant under Abelian p-groups Schmidt, Bernhard Wong, Dai Quan Xiang, Qing School of Physical and Mathematical Sciences Science::Mathematics Group Invariant Matrices Orthogonal Matrices Let a and h be positive integers and let p be a prime. Let q1,…,qt be the distinct prime divisors of h and write Q(h)={∑i=1tciqi:ci∈Z,ci≥0}. We provide constructions of group invariant Butson Hadamard matrices BH(G,h) in the following cases. 1. G=(Zp)2a and at least one of the following conditions is satisfied. • pa∈Q(h), • pa+2∈Q(h) and h is even, • pa+1=(q1−1)(q2−1) where q1 and q2 are distinct prime divisors of h. 2. G=Zpa×Zpa and p−1,p∈Q(h). 3. G=(Zp2)a and pb∈Q(h) for some divisor b of a with 1≤b<a. 4. G=P×Zpa where P is any abelian group of order pa and p∈Q(h). 2022-07-04T01:46:29Z 2022-07-04T01:46:29Z 2021 Journal Article Schmidt, B., Wong, D. Q. & Xiang, Q. (2021). Constructions of Butson Hadamard matrices invariant under Abelian p-groups. Journal of Combinatorial Theory, Series A, 181, 105433-. https://dx.doi.org/10.1016/j.jcta.2021.105433 0097-3165 https://hdl.handle.net/10356/159805 10.1016/j.jcta.2021.105433 2-s2.0-85100678635 181 105433 en Journal of Combinatorial Theory, Series A © 2021 Elsevier Inc. All rights reserved. |
| spellingShingle | Science::Mathematics Group Invariant Matrices Orthogonal Matrices Schmidt, Bernhard Wong, Dai Quan Xiang, Qing Constructions of Butson Hadamard matrices invariant under Abelian p-groups |
| title | Constructions of Butson Hadamard matrices invariant under Abelian p-groups |
| title_full | Constructions of Butson Hadamard matrices invariant under Abelian p-groups |
| title_fullStr | Constructions of Butson Hadamard matrices invariant under Abelian p-groups |
| title_full_unstemmed | Constructions of Butson Hadamard matrices invariant under Abelian p-groups |
| title_short | Constructions of Butson Hadamard matrices invariant under Abelian p-groups |
| title_sort | constructions of butson hadamard matrices invariant under abelian p groups |
| topic | Science::Mathematics Group Invariant Matrices Orthogonal Matrices |
| url | https://hdl.handle.net/10356/159805 |
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