Modelling equidistant frequency permutation arrays: an application of constraints to mathematics

Authors:
Sophie Huczynska;Paul McKay;Ian Miguel;Peter Nightingale
Affiliations:
School of Mathematics and Statistics, University of St Andrews, UK;School of Computer Science, University of St Andrews, UK;School of Computer Science, University of St Andrews, UK;School of Computer Science, University of St Andrews, UK
Venue:
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Year:
2009

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Abstract

Equidistant Frequency Permutation Arrays are combinatorial objects of interest in coding theory. A frequency permutation array is a type of constant composition code in which each symbol occurs the same number of times in each codeword. The problem is to find a set of codewords such that any pair of codewords are a given uniform Hamming distance apart. The equidistant case is of special interest given the result that any optimal constant composition code is equidistant. This paper presents, compares and combines a number of different constraint formulations of this problem class, including a new method of representing permutations with constraints. Using these constraint models, we are able to establish several new results, which are contributing directly to mathematical research in this area.