UT Institute of Computer Science Graduation Theses Topics Registry

Organization

Coding and Information Transmission Group

Abstract

Constacyclic codes are a not much studied generalization of cyclic codes. A linear code C of length n over a finite field F_q is a-constacyclic if for every code word c=(c_0, c_1, ..., c_{n-1}) from C, the word (ac_{n-1}, c_0, c_1, ..., c_{n-2}) is again in C. (Cyclic codes are the case where a=1; and in fact, an a-constacyclic code is an ideal in F_q[x] mod x^n-a. Associated with every such constacyclic code C is a certain longer cyclic code C* and many properties of C can be derived by studying this cyclic code C*. This relation is not new but seems to be little known.
We propose to use this relation to investigate the minimum distance of various classes of constacyclic codes. We will study a few papers where such results are derived to see if they can also be derived in a simpler way by using this relation. Then we will try to design new good constacyclic codes with these ideas in mind.

Graduation Theses defence year

2022-2023

Supervisor

Henk D.L. Hollmann, Vitaly Skachek

Spoken language (s)

English

Requirements for candidates

The topic is suitable both for a bachelor thesis and for a master thesis. Some background in coding theory is probably required. For a master-level thesis some knowledge of linear algebra and algebraic structures would be helpful.

Level

Bachelor, Masters

Keywords

#coding theory, #finite field, minimum Hamming distance, #constacyclic

 

Name

Henk D.L. Hollmann

Phone

+31 619489142

E-mail