On binary codes related to mutually quasi-unbiased weighing matrices

TL;DR

This paper investigates binary codes related to mutually quasi-unbiased weighing matrices, determining their weight distributions, classifying specific codes, and constructing new sets of such matrices for certain parameters.

Contribution

It provides a classification of binary codes satisfying certain conditions and constructs new sets of mutually quasi-unbiased weighing matrices for specific parameters.

Findings

Determined weight distributions of the codes.

Classified binary codes of lengths 8, 16, and maximal length 32.

Constructed new sets of mutually quasi-unbiased weighing matrices.

Abstract

Some mutually quasi-unbiased weighing matrices are constructed from binary codes satisfying certain conditions. Motivated by this, in this note, we study binary codes satisfying the conditions. The weight distributions of binary codes satisfying the conditions are determined. We also give a classification of binary codes of lengths $8,16$ and binary maximal codes of length $32$ satisfying the conditions. As an application, sets of $8$ mutually quasi-unbiased weighing matrices for parameters $(16,16,4,64)$ and $4$ mutually quasi-unbiased weighing matrices for parameters $(32,32,4,256)$ are constructed for the first time.