On the classification of weighing matrices and self-orthogonal codes

TL;DR

This paper introduces a classification method for weighing matrices using self-orthogonal codes, successfully classifying matrices up to order 17 and revising known classifications, including weight 5 matrices and certain ternary codes.

Contribution

It presents a novel classification approach linking weighing matrices to self-orthogonal codes, extending classifications to new orders and weights.

Findings

Classified weighing matrices of orders up to 15 and 17

Revised classification of weight 5 weighing matrices

Updated classification of ternary self-orthogonal codes of lengths 18 and 19

Abstract

We provide a classification method of weighing matrices based on a classification of self-orthogonal codes. Using this method, we classify weighing matrices of orders up to 15 and order 17, by revising some known classification. In addition, we give a revised classification of weighing matrices of weight 5. A revised classification of ternary maximal self-orthogonal codes of lengths 18 and 19 is also presented.