Symmetric Designs Attached to Four-Weight Spin Models

Authors:
Etsuko Bannai;Mitsuhiro Sawano
Affiliations:
Graduate School of Mathematics, Kyushu University, 6-10-1, Hakozaki, Higashi-Ku, Fukuoka, 812-8581, Japan;Graduate School of Mathematics, Kyushu University, 6-10-1, Hakozaki, Higashi-Ku, Fukuoka, 812-8581, Japan
Venue:
Designs, Codes and Cryptography
Year:
2002

Citing 6
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Abstract

H. Guo and T. Huang studied the four-weight spin models (X, W_1, W_2, W_3, W_4;D) with the property that the entries of the matrix W_2 (or equivalently W_4) consist of exactly two distinct values. They found that such spin models are always related to symmetric designs whose derived design with respect to any block is a quasi symmetric design. In this paper we show that such a symmetric design admits a four-weight spin model with exactly two values on W_2 if and only if it has some kind of duality between the set of points and the set of blocks. We also give some examples of parameters of symmetric designs which possibly admit four-weight spin models with exactly two values on W_2.