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