Uniqueness of certain association schemes

Authors:
Eiichi Bannai;Etsuko Bannai;Hideo Bannai
Affiliations:
Faculty of Mathematics, Graduate School, Kyushu University, Hakozaki 6-10-1, Higashi-ku, Fukuoka 812-8581, Japan;Faculty of Mathematics, Graduate School, Kyushu University, Hakozaki 6-10-1, Higashi-ku, Fukuoka 812-8581, Japan;Department of Informatics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
Venue:
European Journal of Combinatorics
Year:
2008

Citing 2
Cited 3

Three-Class Association Schemes

Journal of Algebraic Combinatorics: An International Journal
Association Schemes Related to Kasami Codes and KerdockSets

Designs, Codes and Cryptography

Few-cosine spherical codes and Barnes--Wall lattices

Journal of Combinatorial Theory Series A
Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets

Journal of Combinatorial Theory Series A
A survey on spherical designs and algebraic combinatorics on spheres

European Journal of Combinatorics

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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 R^1^0 and the other one is the class 3 association scheme with 64 vertices in R^1^4. We prove the uniqueness mainly by geometric considerations with some computational help.