Orderly Generation of Butson Hadamard Matrices

Pekka H. J. Lampio; Patric R. J. Ostergard; Ferenc Szollosi

doi:10.1090/mcom/3453

Orderly Generation of Butson Hadamard Matrices

Pekka H. J. Lampio^*, Patric R. J. Ostergard, Ferenc Szollosi

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

In this paper Butson-type complex Hadamard matrices BH(n, q) of order n over the complex qth roots of unity are classified for small parameters by computer-aided methods. The results include a classification of BH(21, 3), BH(16, 4), and BH(14, 6) matrices. There are exactly 72, 1786763, and 167776 such matrices, respectively, up to monomial equivalence. Additionally, an example of a BH(14, 10) matrix is shown for the first time, and the nonexistence of BH(8, 15), BH(11, q) for q is an element of {10, 14, 15}, and BH(13, 15) matrices is proved.

Original language	English
Pages (from-to)	313-331
Number of pages	19
Journal	Mathematics of Computation
Volume	89
Issue number	321
DOIs	https://doi.org/10.1090/mcom/3453
Publication status	Published - Jan 2020
MoE publication type	A1 Journal article-refereed

Keywords

CLASSIFICATION
EXISTENCE

Access to Document

10.1090/mcom/3453

https://arxiv.org/abs/1707.02287

Dataset for Orderly Generation of Butson Hadamard Matrices
Lampio, P. (Creator), Östergård, P. (Creator) & Szollosi, F. (Creator), Zenodo, 13 Mar 2019
DOI: 10.5281/zenodo.2585766
Dataset

Construction and Classification of Discrete Mathematic Structures
Kokkala, J. (Project Member), Laaksonen, A. (Project Member), Östergård, P. (Principal investigator), Szollosi, F. (Project Member), Pöllänen, A. (Project Member), Ganzhinov, M. (Project Member) & Heinlein, D. (Project Member)
01/09/2015 → 31/08/2019
Project: Academy of Finland: Other research funding

Cite this

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title = "Orderly Generation of Butson Hadamard Matrices",

abstract = "In this paper Butson-type complex Hadamard matrices BH(n, q) of order n over the complex qth roots of unity are classified for small parameters by computer-aided methods. The results include a classification of BH(21, 3), BH(16, 4), and BH(14, 6) matrices. There are exactly 72, 1786763, and 167776 such matrices, respectively, up to monomial equivalence. Additionally, an example of a BH(14, 10) matrix is shown for the first time, and the nonexistence of BH(8, 15), BH(11, q) for q is an element of {10, 14, 15}, and BH(13, 15) matrices is proved.",

keywords = "CLASSIFICATION, EXISTENCE",

author = "Lampio, {Pekka H. J.} and Ostergard, {Patric R. J.} and Ferenc Szollosi",

year = "2020",

month = jan,

doi = "10.1090/mcom/3453",

language = "English",

volume = "89",

pages = "313--331",

journal = "Mathematics of Computation",

issn = "0025-5718",

publisher = "American Mathematical Society",

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TY - JOUR

T1 - Orderly Generation of Butson Hadamard Matrices

AU - Lampio, Pekka H. J.

AU - Ostergard, Patric R. J.

AU - Szollosi, Ferenc

PY - 2020/1

Y1 - 2020/1

N2 - In this paper Butson-type complex Hadamard matrices BH(n, q) of order n over the complex qth roots of unity are classified for small parameters by computer-aided methods. The results include a classification of BH(21, 3), BH(16, 4), and BH(14, 6) matrices. There are exactly 72, 1786763, and 167776 such matrices, respectively, up to monomial equivalence. Additionally, an example of a BH(14, 10) matrix is shown for the first time, and the nonexistence of BH(8, 15), BH(11, q) for q is an element of {10, 14, 15}, and BH(13, 15) matrices is proved.

AB - In this paper Butson-type complex Hadamard matrices BH(n, q) of order n over the complex qth roots of unity are classified for small parameters by computer-aided methods. The results include a classification of BH(21, 3), BH(16, 4), and BH(14, 6) matrices. There are exactly 72, 1786763, and 167776 such matrices, respectively, up to monomial equivalence. Additionally, an example of a BH(14, 10) matrix is shown for the first time, and the nonexistence of BH(8, 15), BH(11, q) for q is an element of {10, 14, 15}, and BH(13, 15) matrices is proved.

KW - CLASSIFICATION

KW - EXISTENCE

U2 - 10.1090/mcom/3453

DO - 10.1090/mcom/3453

M3 - Article

SN - 0025-5718

VL - 89

SP - 313

EP - 331

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 321

ER -

Orderly Generation of Butson Hadamard Matrices

Abstract

Keywords

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Dataset for Orderly Generation of Butson Hadamard Matrices

Projects

Construction and Classification of Discrete Mathematic Structures

Cite this