Weighing matrices and spherical codes
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.
weighing matrices mutually unbiased weighing matrices root system kerdock codes over \(\mathbb {z}_{4}\)