Liam PolkinghorneLiam Polkinghorne

Queensland University of Technology


I’ve studied at QUT doing a Bachelor of Mathematics in a Dean’s Scholar program and with a Vice Chancellor Scholarship. I’ve an interest in Discrete Mathematics and Pure Mathematics in the main areas of Topolgy and Number theory. My specialisations are in Operations Research and Computational Mathematics. My honours project will be in Discrete Mathematics and one day hope to move on to a PHD in the same field.

Nonlinear Codes of Length 4 on 4 Symbols

Error Correcting Codes are a mechanism used to enable robust communication across noisy mediums. The wide array of digital communication methods used in modern life requires a wide array of error correction methods. It is known that there exist nonlinear codes which have better error correction capability than Linear Codes. However, the known implementation algorithms for nonlinear codes are less efficient. Hence nonlinear codes are not as well studied. The aim of this project is to investigate properties of nonlinear codes of length 4 on 4 Symbols with particular focus on the covering radius. Techniques will include using graphs to represent aspects of the codes. These Techniques have previously been applied to codes of length 3 on 4 symbols, and have shown to be useful in determining the covering radius.

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