Harmonic index designs in binary Hamming schemes
type: Item
instance of: scholarly article
title: Harmonic index designs in binary Hamming schemes
zbMATH Open document ID: 1387.05035
author: Yan Zhu
author: Eiichi Bannai
author: Etsuko Bannai
author: Kyoung-Tark Kim
author: Ikuta, Takuya
published in: Graphs and Combinatorics
publication date: 2018-02-14T00:00:00Z
review text: We recall the ``addition formula'' for a commutative association scheme. From this formula we construct a linear programming for the size of harmonic index designs and define the notion of tight designs using Fisher type inequality. We examine the existence of tight harmonic index \(T\)-designs for some \(T\) in binary Hamming association schemes \(H(d, 2)\). The non-existence of tight harmonic index \(T\)-designs in binary Hamming schemes \(H(d, 2)\) for \(T = \{4\}, \{6\}, \{8, 4\}, \{8, 2\}, \{6, 4\}\) and \(\{6, 2\}\) was showed and the asymptotic (i.e., \(d \rightarrow \infty\)) non-existence of tight designs of harmonic index \(T = \{2e\}\) for \(e \geq 4\) was proved. A necessary and sufficient condition for the existence of tight harmonic index \(\{2\}\)-designs was provided and some tight harmonic index \(\{4, 2\}\)-designs in \(H(6, 2)\) which are any half part of the tight 5-design in \(H(6, 2)\) was found.
reviewed by: Ioan Tomescu
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 6838840
zbMATH Keywords: harmonic index design
zbMATH Keywords: Hamming association scheme
zbMATH Keywords: addition formula
zbMATH Keywords: Fisher type lower bound
zbMATH Keywords: tight design
describes a project that uses: SageMath
MaRDI profile type: Publication
full work available at URL: s00373-017-1784-5
OpenAlex ID: W2617248598
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DOI: 10.1007/S00373-017-1784-5
description: scientific article; zbMATH DE number 6838840