Counting Codes via the Container Method

Date

2024

Authors

Penney, Amy

Journal Title

Journal ISSN

Volume Title

Publisher

University of Victoria

Abstract

The container method is a technique used to upper bound the number of independent sets in a graph. The technique originated from Kleitman and Winston, and Sapozheko. It was developed in full generality and extended to hypergraphs independently by Saxton and Thomason, and Balogh, Morris and Samotij. This technique has been used by Balogh, Treglown and Wagner to prove an upper bound on the number of t error correcting codes, as well as a bound on the number of r-(n,k,d) codes when r=2. The goal of this project is to extend these results to upper bound the number of r-(n,k,d) codes for general r.

Description

Keywords

Container Method, r-(n,k,d) Codes, Error Correcting Codes

Citation