## Repeat-free codes

Organization

Coding and Information Transmission Group

Abstract

In this thesis topic we are going to investigate repeat-free codes. A word c of length n over a finite alphabet A is called (n,k) repeat-free if every word of length k occurs at most once as a subword of c. Here a word w=w_1w_2...w_k occurs in c at location i if c_{i+j-1}=w_j for j=1, ..., k. A collection C of words of length n over A is called an (n,k) repeat-free code over A if every word c in C is (n,k)-repeat-free. More general, a code C is called (n,k) (t+1)-repeat-free if in each code word, every word of length k occurs at most t times.

Some important questions are the following.

1. What is the number N_{n,k} of (n,k) repeat-free words of length n? And what is

the number N_{n,k,t} of (n; k) (t + 1)-repeat-free words?

2. How should we encode into repeat-free words?

Already the notion of a (t + 1)-repeat-free code seems new here.

The aim is to read some papers on this subject and then to investigate the above questions.

Some important questions are the following.

1. What is the number N_{n,k} of (n,k) repeat-free words of length n? And what is

the number N_{n,k,t} of (n; k) (t + 1)-repeat-free words?

2. How should we encode into repeat-free words?

Already the notion of a (t + 1)-repeat-free code seems new here.

The aim is to read some papers on this subject and then to investigate the above questions.

Graduation Theses defence year

2022-2023

Supervisor

Henk D.L. Hollmann, Vitaly Skachek, Ago-Erik Riet

Spoken language (s)

English

Requirements for candidates

The topic is suitable both for a bachelor thesis and for a master thesis.

Some background in combinatorics would be helpful but is not required.

Some background in combinatorics would be helpful but is not required.

Level

Bachelor, Masters

Keywords

### Application of contact

Name

Henk D.L. Hollmann

Phone

+31 619489142

E-mail