Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets
Association schemes related to universally optimal configurations, Kerdock codes and extremal Euclidean line-sets
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DOI：
10.1016/j.jcta.2008.07.002
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发表时间：
2008-02
期刊：
影响因子：
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通讯作者：
K. Abdukhalikov;E. Bannai;Sho Suda
中科院分区：
文献类型：
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作者：
K. Abdukhalikov;E. Bannai;Sho Suda
H. Cohn等人在r14中提出了64个点的关联方案，该方案被推测为普遍最优码。我们证明了该方案在Kerdock码和实数互无偏基的极大集合方面具有泛化性。这些格式也与欧几里德空间和Barnes-Wall格中的极值行集有关。D. de Caen和E.R. van Dam构造了两个无穷级数的正式对偶3类关联方案。我们通过构造与四元线性Kerdock码和Preparata码相关的两个对偶阿贝尔格式来解释这种形式对偶性。
H. Cohn et al. proposed an association scheme of 64 points in R14which 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 Kerdock and Preparata codes.