Geodesic
Weighing matrices and spherical codes
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 1, pp. 283-291.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Mutually unbiased weighing matrices (MUWM) are closely related to an antipodal spherical code with 4 angles. In this paper, we clarify the relation between MUWM and the spherical codes and determine the maximum size of a set of MUWM with weight 4 for any order. Moreover, we define mutually quasi-unbiased weighing matrices (MQUWM) as a natural generalization of MUWM from the viewpoint of spherical codes. We determine the maximum size of a set of MQUWM for the parameters $(d,2,4,1)$ and $(d,d,d/2,2d)$. This includes an affirmative answer to the problem of Best, Kharaghani, and Ramp.
Classification : 05B20, 94B25
Keywords: weighing matrices, mutually unbiased weighing matrices, root system, Kerdock codes over $\mathbb Z_4$ 
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     title = {Weighing matrices and spherical codes},
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Nozaki, Hiroshi; Suda, Sho. Weighing matrices and spherical codes. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 1, pp. 283-291. http://geodesic.mathdoc.fr/item/JAC_2015__42_1_a1/