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...

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Main Authors: Schmidt, Bernhard, Wong, Dai Quan, Xiang, Qing
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2022
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Online Access:https://hdl.handle.net/10356/159805
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spelling sg-ntu-dr.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.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
Group Invariant Matrices
Orthogonal Matrices
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
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).
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Schmidt, Bernhard
Wong, Dai Quan
Xiang, Qing
format Article
author Schmidt, Bernhard
Wong, Dai Quan
Xiang, Qing
author_sort Schmidt, Bernhard
title Constructions of Butson Hadamard matrices invariant under Abelian p-groups
title_short 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_sort constructions of butson hadamard matrices invariant under abelian p-groups
publishDate 2022
url https://hdl.handle.net/10356/159805
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