## Repeat-free codes

Organisatsiooni nimi

Coding and Information Transmission Group

Kokkuvõte

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.

Lõputöö kaitsmise aasta

2022-2023

Juhendaja

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

Suhtlemiskeel(ed)

inglise keel

Nõuded kandideerijale

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.

Tase

Bakalaureus, Magister

Märksõnad

### Kandideerimise kontakt

Nimi

Henk D.L. Hollmann

Tel

+31 619489142

E-mail