An efficient string sorting algorithm for weighing matrices of small weight

It is demonstrated that the search for weighing matrices of small weights constructed from two circulants can be viewed as a string sorting problem together with a linear time algorithm to locate common strings in two sorted arrays.

Abstract

In this paper, we demonstrate that the search for weighing matrices of small weights constructed from two circulants can be viewed as a string sorting problem together with a linear time algorithm to locate common strings in two sorted arrays. We also introduce a sparse encoding of the periodic autocorrelation function vector, based on concepts from Algorithmic Information Theory, also known as Kolmogorov complexity, that allows us to speed up the algorithm considerably. Finally, we use these ideas to find new weighing matrices W(2 center dot n, 9) constructed from two circulants, for many values of n in the range 100 a parts per thousand currency signA n a parts per thousand currency signA 300. These matrices are given here for the first time. We also discuss briefly a connection with Combinatorial Optimization.