Uniqueness of certain association schemes

Eiichi Bannai; Etsuko Bannai; Hideo Bannai

doi:10.1016/j.ejc.2007.06.016

Uniqueness of certain association schemes

Eiichi Bannai, Etsuko Bannai, Hideo Bannai

Mathematical Informatics

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6 Citations (Scopus)

Abstract

We prove the uniqueness of the two association schemes which appear in recent work of Henry Cohn and others in connection with their study of universally optimal spherical codes in Euclidean spaces: one is the class 4 association scheme with 40 vertices in R¹⁰ and the other one is the class 3 association scheme with 64 vertices in R¹⁴. We prove the uniqueness mainly by geometric considerations with some computational help.

Original language	English
Pages (from-to)	1379-1395
Number of pages	17
Journal	European Journal of Combinatorics
Volume	29
Issue number	6
DOIs	https://doi.org/10.1016/j.ejc.2007.06.016
Publication status	Published - Aug 2008

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2007.06.016

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title = "Uniqueness of certain association schemes",

abstract = "We prove the uniqueness of the two association schemes which appear in recent work of Henry Cohn and others in connection with their study of universally optimal spherical codes in Euclidean spaces: one is the class 4 association scheme with 40 vertices in R10 and the other one is the class 3 association scheme with 64 vertices in R14. We prove the uniqueness mainly by geometric considerations with some computational help.",

author = "Eiichi Bannai and Etsuko Bannai and Hideo Bannai",

year = "2008",

month = aug,

doi = "10.1016/j.ejc.2007.06.016",

language = "English",

volume = "29",

pages = "1379--1395",

journal = "European Journal of Combinatorics",

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publisher = "Academic Press Inc.",

number = "6",

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TY - JOUR

T1 - Uniqueness of certain association schemes

AU - Bannai, Eiichi

AU - Bannai, Etsuko

AU - Bannai, Hideo

PY - 2008/8

Y1 - 2008/8

N2 - We prove the uniqueness of the two association schemes which appear in recent work of Henry Cohn and others in connection with their study of universally optimal spherical codes in Euclidean spaces: one is the class 4 association scheme with 40 vertices in R10 and the other one is the class 3 association scheme with 64 vertices in R14. We prove the uniqueness mainly by geometric considerations with some computational help.

AB - We prove the uniqueness of the two association schemes which appear in recent work of Henry Cohn and others in connection with their study of universally optimal spherical codes in Euclidean spaces: one is the class 4 association scheme with 40 vertices in R10 and the other one is the class 3 association scheme with 64 vertices in R14. We prove the uniqueness mainly by geometric considerations with some computational help.

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U2 - 10.1016/j.ejc.2007.06.016

DO - 10.1016/j.ejc.2007.06.016

M3 - Article

AN - SCOPUS:43849087964

SN - 0195-6698

VL - 29

SP - 1379

EP - 1395

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 6

ER -

Uniqueness of certain association schemes

Abstract

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