||Weighing matrices and spherical codes
Nozaki, Hiroshi ,
Journal of algebraic combinatorics
291 , 2015-08 , Springer
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.