Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:116

Article

Abdukhalikov, Kanat¹  Bannai, Eiichi²  Suda, Sho³ 

[1] Inst Math, Alma Ata 050010, Kazakhstan

[2] Kyushu Univ, Grad Sch Math, Higashi Ku, Fukuoka 8128581, Japan

[3] Tohoku Univ, Grad Sch Informat Sci, Sendai, Miyagi 6808570, Japan

关键词: Universally optimal configurations;    Association schemes;    Dual schemes;    Kerdock codes;    Preparata codes;    Mutually unbiased bases;    Barnes-Wall lattices;   

DOI  :  10.1016/j.jcta.2008.07.002

来源: Elsevier

【 摘 要 】

H. Cohn et al. proposed an association scheme of 64 points in R 14 which is conjectured to be a universally optimal code. We show that this scheme has a generalization in terms of Kerdock codes, as well as in terms of maximal collections of real mutually unbiased bases. These schemes are also related to extremal line-sets in Euclidean spaces and Barnes-Wall lattices. D. de Caen and E.R. van Dam constructed two infinite series of formally dual 3-class association schemes. We explain this formal duality by constructing two dual abelian schemes related to quaternary linear Kerclock and Preparata codes. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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