Please use this identifier to cite or link to this item: http://buratest.brunel.ac.uk/handle/2438/7495
Title: Integral zeroes of Krawtchouk polynomials
Authors: Alenezi, Ahmad M
Advisors: Krasikov, I
Keywords: Hamming schemes;Graph representation;Combinatorial structures;Coding theory;Discrete mathematics
Issue Date: 2012
Publisher: Brunel University, School of Information Systems, Computing and Mathematics
Abstract: Krawtchouk polynomials appear in many various areas of mathematics starting from discrete mathematics (e.g., in coding theory), association schemes, and in the theory of graph representations. The existence/non-existence of integral zeroes of these polynomials is crucial for the existence/non-existence of combinatorial structures in the Hamming association schemes. The integer zeroes of Krawtchouk polynomials for k = 4; 5; 6 and 7 have been found using some very recent results on solvability of polynomial diophantine equations. Our aim is two-fold: Firstly, to verify these results using extensive computer calculations. This requires the solution of some of Pell’s equations and the use of the symbolic mathematics software mathematica. Secondly, we numerically investigate a conjecture dealing with the integer zeroes of the Krawtchouk polynomials Pm2 (m^2) (x) and provide confirmation of the conjecture using a combination of approaches up to m <= 1000, i.e., for the polynomials up to degree of about half a million.
Description: This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.
URI: http://bura.brunel.ac.uk/handle/2438/7495
Appears in Collections:Dept of Mathematics Theses
Mathematical Sciences

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