Mappings of Butson-type Hadamard matrices

Patric R.J. Östergård; William T. Paavola

doi:10.1016/j.disc.2018.05.012

Mappings of Butson-type Hadamard matrices

Patric R.J. Östergård^*, William T. Paavola

^*Tämän työn vastaava kirjoittaja

Information Theory

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

4 Sitaatiot (Scopus)

111 Lataukset (Pure)

Abstrakti

A BH(q,n) Butson-type Hadamard matrix H is an n×n matrix over the complex qth roots of unity that fulfils HH^∗=nI_n. It is well known that a BH(4,n) matrix can be used to construct a BH(2,2n) matrix, that is, a real Hadamard matrix. This method is here generalised to construct a BH(q,pn) matrix from a BH(pq,n) matrix, where q has at most two distinct prime divisors, one of them being p. Moreover, an algorithm for finding the domain of the mapping from its codomain in the case p=q=2 is developed and used to classify the BH(4,16) matrices from a classification of the BH(2,32) matrices.

Alkuperäiskieli	Englanti
Sivut	2387-2397
Sivumäärä	11
Julkaisu	Discrete Mathematics
Vuosikerta	341
Numero	9
DOI - pysyväislinkit	https://doi.org/10.1016/j.disc.2018.05.012
Tila	Julkaistu - 1 syysk. 2018
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Pääsy asiakirjaan

10.1016/j.disc.2018.05.012

ELEC-ostergard-et-al-mappings_of_bustopaper_20180514Accepted author manuscript, 287 KBLisenssi: CC BY-NC-ND

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Link to publication in Scopus

Konstruktion och klassificering av diskreta matematiska strukturer
Kokkala, J. (Projektin jäsen), Laaksonen, A. (Projektin jäsen), Östergård, P. (Vastuullinen tutkija), Szollosi, F. (Projektin jäsen), Pöllänen, A. (Projektin jäsen), Ganzhinov, M. (Projektin jäsen) & Heinlein, D. (Projektin jäsen)
01/09/2015 → 31/08/2019
Projekti: Academy of Finland: Other research funding

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title = "Mappings of Butson-type Hadamard matrices",

abstract = "A BH(q,n) Butson-type Hadamard matrix H is an n×n matrix over the complex qth roots of unity that fulfils HH∗=nIn. It is well known that a BH(4,n) matrix can be used to construct a BH(2,2n) matrix, that is, a real Hadamard matrix. This method is here generalised to construct a BH(q,pn) matrix from a BH(pq,n) matrix, where q has at most two distinct prime divisors, one of them being p. Moreover, an algorithm for finding the domain of the mapping from its codomain in the case p=q=2 is developed and used to classify the BH(4,16) matrices from a classification of the BH(2,32) matrices.",

keywords = "Butson-type Hadamard matrix, Classification, Complex matrix, Mapping, Monomial equivalence",

author = "{\"O}sterg{\aa}rd, {Patric R.J.} and Paavola, {William T.}",

year = "2018",

month = sep,

day = "1",

doi = "10.1016/j.disc.2018.05.012",

language = "English",

volume = "341",

pages = "2387--2397",

journal = "Discrete Mathematics",

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TY - JOUR

T1 - Mappings of Butson-type Hadamard matrices

AU - Östergård, Patric R.J.

AU - Paavola, William T.

PY - 2018/9/1

Y1 - 2018/9/1

N2 - A BH(q,n) Butson-type Hadamard matrix H is an n×n matrix over the complex qth roots of unity that fulfils HH∗=nIn. It is well known that a BH(4,n) matrix can be used to construct a BH(2,2n) matrix, that is, a real Hadamard matrix. This method is here generalised to construct a BH(q,pn) matrix from a BH(pq,n) matrix, where q has at most two distinct prime divisors, one of them being p. Moreover, an algorithm for finding the domain of the mapping from its codomain in the case p=q=2 is developed and used to classify the BH(4,16) matrices from a classification of the BH(2,32) matrices.

AB - A BH(q,n) Butson-type Hadamard matrix H is an n×n matrix over the complex qth roots of unity that fulfils HH∗=nIn. It is well known that a BH(4,n) matrix can be used to construct a BH(2,2n) matrix, that is, a real Hadamard matrix. This method is here generalised to construct a BH(q,pn) matrix from a BH(pq,n) matrix, where q has at most two distinct prime divisors, one of them being p. Moreover, an algorithm for finding the domain of the mapping from its codomain in the case p=q=2 is developed and used to classify the BH(4,16) matrices from a classification of the BH(2,32) matrices.

KW - Butson-type Hadamard matrix

KW - Classification

KW - Complex matrix

KW - Mapping

KW - Monomial equivalence

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U2 - 10.1016/j.disc.2018.05.012

DO - 10.1016/j.disc.2018.05.012

M3 - Article

AN - SCOPUS:85048461397

SN - 0012-365X

VL - 341

SP - 2387

EP - 2397

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 9

ER -

Mappings of Butson-type Hadamard matrices

Abstrakti

Pääsy asiakirjaan

Muut tiedostot ja linkit

Sormenjälki

Projektit

Konstruktion och klassificering av diskreta matematiska strukturer

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