Topics in Coding Theory: 1. The A(,s)(n,d) Problem in The Plotkin Region. 2. Number of Information Symbols in a Bch Code

In chapter 1 we investigate the A(,s)(n,d) problem in the Plotkin Region. The problem is to finding the maximum number of codewords in a code on an alphabet with s symbols that has length n and minimum Hamming distance d. The Plotkin Region is the set of n and d such that sd > t(s - 1)n. We define Generalized Hadamard matrices, using a notion of orthogonality over a group, and show that these matrices give rise to certain A(,s)(n,d) codes. Two general constructions for A(,s)(n,d) codes, which apparently do not depend on Hadamard matrices, are given. Lastly we discuss a computer implemented algorithm to search for A(,3)(15,11).

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Merkey, Phillip Roy

• Mathematics

Identifier

(UMI)AAI8701565

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71245