Application of Orthogonal Polynomials and Special Matrices to Orthogonal Arrays
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Special matrices are explored in many areas of science and technology. Krawtchouk matrix is such a matrix that plays important role in coding theory and theory of orthogonal arrays also called fractional factorial designs in planning of experiments and statistics. In this paper we give explicitly Smith normal forms of Krawtchouk matrix and its extended matrix. Also we propose a computationally effective method for determining the Hamming distance distributions of an orthogonal array with given parameters. The obtained results facilitate the solving of many existence and classification problems in theory of codes and orthogonal arrays.
KeywordsOrthogonal polynomials Smith normal form Distance distribution Orthogonal arrays Linear programming bound
This work has been accomplished with the financial support of the Ministry of Education and Science of Bulgaria by the Grant No. D01-221/03.12.2018 for National Centre of High-performance and Distributed Computing—part of the Bulgarian National Roadmap on RIs.
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