Hamming graphs in Nomura algebras

Ada Chan; Akihiro Munemasa

doi:10.1016/j.laa.2011.01.020

Hamming graphs in Nomura algebras

Ada Chan, Akihiro Munemasa

INF - Computer and Mathematical Sciences

York University Toronto

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

Abstract

Let A be an association scheme on q ≥ 3 vertices. We show that the Bose-Mesner algebra of the generalized Hamming scheme H(n,A), for n ≥ 2, is not the Nomura algebra of any type II matrix. This result gives examples of formally self-dual Bose-Mesner algebras that are not the Nomura algebras of type II matrices.

Original language	English
Pages (from-to)	330-341
Number of pages	12
Journal	Linear Algebra and Its Applications
Volume	435
Issue number	2
DOIs	https://doi.org/10.1016/j.laa.2011.01.020
Publication status	Published - 2011 Jul 15

Keywords

Duality of association scheme
Hamming scheme
Nomura algebra
Type II matrix

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10.1016/j.laa.2011.01.020

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title = "Hamming graphs in Nomura algebras",

abstract = "Let A be an association scheme on q ≥ 3 vertices. We show that the Bose-Mesner algebra of the generalized Hamming scheme H(n,A), for n ≥ 2, is not the Nomura algebra of any type II matrix. This result gives examples of formally self-dual Bose-Mesner algebras that are not the Nomura algebras of type II matrices.",

keywords = "Duality of association scheme, Hamming scheme, Nomura algebra, Type II matrix",

author = "Ada Chan and Akihiro Munemasa",

note = "Funding Information: Corresponding author. E-mail addresses: ssachan@yorku.ca (A. Chan), munemasa@math.is.tohoku.ac.jp (A. Munemasa). 1 The first author gratefully acknowledges the support from a JSPS postdoctoral fellowship and a NSERC discovery grant.",

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AU - Chan, Ada

AU - Munemasa, Akihiro

N1 - Funding Information: Corresponding author. E-mail addresses: ssachan@yorku.ca (A. Chan), munemasa@math.is.tohoku.ac.jp (A. Munemasa). 1 The first author gratefully acknowledges the support from a JSPS postdoctoral fellowship and a NSERC discovery grant.

PY - 2011/7/15

Y1 - 2011/7/15

N2 - Let A be an association scheme on q ≥ 3 vertices. We show that the Bose-Mesner algebra of the generalized Hamming scheme H(n,A), for n ≥ 2, is not the Nomura algebra of any type II matrix. This result gives examples of formally self-dual Bose-Mesner algebras that are not the Nomura algebras of type II matrices.

AB - Let A be an association scheme on q ≥ 3 vertices. We show that the Bose-Mesner algebra of the generalized Hamming scheme H(n,A), for n ≥ 2, is not the Nomura algebra of any type II matrix. This result gives examples of formally self-dual Bose-Mesner algebras that are not the Nomura algebras of type II matrices.

KW - Duality of association scheme

KW - Hamming scheme

KW - Nomura algebra

KW - Type II matrix

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VL - 435

SP - 330

EP - 341

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 2

ER -

Hamming graphs in Nomura algebras

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Keywords

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