Partitions of codes

Waugh, Karl Michael Vincent (2013) Partitions of codes. Doctoral thesis (PhD), University of Sussex.

[img]
Preview
PDF - Published Version
Download (1MB) | Preview

Abstract

In this thesis we look at coding theory wherein we introduce the concept of perspective, a generalisation on the minimum distance of a code, which naturally leads to a partition
of the code. Subsequently we introduce focused splittings, which shall be shown to be a generalisation of perfect codes. We investigate the existence of such objects, and address questions such as the complexity of finding a focused splittings, which we show to be NPComplete. We analyse the symmetries of focused splittings. We use focused splittings to address the problem of error correction and we construct an encoding method based on them. Finally we test this construction for various classes of focused splittings.

Item Type: Thesis (Doctoral)
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0075 Electronic computers. Computer science
Depositing User: Library Cataloguing
Date Deposited: 06 Jun 2013 12:50
Last Modified: 15 Sep 2015 12:11
URI: http://sro.sussex.ac.uk/id/eprint/45301

View download statistics for this item

📧 Request an update