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

Information Theory

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., Laaksonen, A., Östergård, P., Szollosi, F., Pöllänen, A., Ganzhinov, M. & Heinlein, D.
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