An algebraic approach to graph codes

Fernando Pinero

Research output: Book/ReportPh.D. thesis

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Abstract

This thesis consists of six chapters. The first chapter, contains a short introduction to coding theory in which we explain the coding theory concepts we use. In the second chapter, we present the required theory for evaluation codes and also give an example of some fundamental codes in coding theory as evaluation codes. Chapter three consists of the introduction to graph based codes, such as Tanner codes and graph codes. In Chapter four, we compute the dimension of some graph based codes with a result combining graph based codes and subfield subcodes. Moreover, some codes in chapter four are optimal or best known for their parameters. In chapter five we study some graph codes with Reed–Solomon component codes. The underlying graph is well known and widely used for its good characteristics. This helps us to compute the dimension of the graph codes. We also introduce a combinatorial concept related to the iterative encoding of graph codes with MDS component code. The last chapter deals with affine Grassmann codes and Grassmann codes. We begin with some previously known codes and prove that they are also Tanner codes of the incidence graph of the point–line partial geometry of the Grassmannian. We expect that the techniques exposed in chapter six are also applicable to other codes as well.
Original languageEnglish
Place of PublicationKgs. Lyngby
PublisherTechnical University of Denmark
Number of pages96
Publication statusPublished - 2015
SeriesDTU Compute PHD-2014
Number352
ISSN0909-3192

Projects

Graph Codes

Pinero, F., Beelen, P., Chen, H., Bossert, M., Roth, R. M., Geil, H. O. & Høholdt, T.

Grundforskningsfonden

01/08/201123/01/2015

Project: PhD

Cite this

Pinero, F. (2015). An algebraic approach to graph codes. Technical University of Denmark. DTU Compute PHD-2014, No. 352