scholarly journals Characterization of p-ary functions in terms of association schemes and its applications

2022 ◽  
Vol 187 ◽  
pp. 105576
Author(s):  
Yansheng Wu ◽  
Jong Yoon Hyun ◽  
Yoonjin Lee
Keyword(s):  
Association Schemes

scholarly journals Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4

2018 ◽  
Vol 6 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Takuya Ikuta ◽  
Akihiro Munemasa
Keyword(s):  
Association Scheme ◽  
Hadamard Matrix ◽  
Hadamard Matrices ◽  
Association Schemes ◽  
Roots Of Unity ◽  
Galois Rings ◽  
Type Complex ◽  
Complex Hadamard Matrix

Abstract We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes. First, we give a characterization of the eigenmatrix of a commutative nonsymmetric association scheme of class 3 whose Bose-Mesner algebra contains a nonsymmetric hermitian complex Hadamard matrix, and show that such a complex Hadamard matrix is necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.We also give nonsymmetric association schemes X of class 6 on Galois rings of characteristic 4, and classify hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of X. It is shown that such a matrix is again necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.

scholarly journals On Relative $t$-Designs in Polynomial Association Schemes

10.37236/4889 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Eiichi Bannai ◽  
Etsuko Bannai ◽  
Sho Suda ◽  
Hajime Tanaka
Keyword(s):  
Lower Bounds ◽  
Association Scheme ◽  
Point Of View ◽  
Association Schemes ◽  
Algebraic Characterization ◽  
Terwilliger Algebra ◽  
C Algebra ◽  
Irreducible Modules

Motivated by the similarities between the theory of spherical $t$-designs and that of $t$-designs in $Q$-polynomial association schemes, we study two versions of relative $t$-designs, the counterparts of Euclidean $t$-designs for $P$- and/or $Q$-polynomial association schemes. We develop the theory based on the Terwilliger algebra, which is a noncommutative associative semisimple $\mathbb{C}$-algebra associated with each vertex of an association scheme. We compute explicitly the Fisher type lower bounds on the sizes of relative $t$-designs, assuming that certain irreducible modules behave nicely. The two versions of relative $t$-designs turn out to be equivalent in the case of the Hamming schemes. From this point of view, we establish a new algebraic characterization of the Hamming schemes.

scholarly journals Characterization of association schemes by equitable partitions

2006 ◽  
Vol 27 (2) ◽  
pp. 139-152 ◽  
Author(s):  
Mitsugu Hirasaka ◽  
Hanguk Kang ◽  
Kijung Kim
Keyword(s):  
Association Schemes
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