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Linear Codes with Constrained Generator Matrices

Citation

Yildiz, Hikmet (2021) Linear Codes with Constrained Generator Matrices. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/qz6m-wp22. https://resolver.caltech.edu/CaltechTHESIS:05242021-223430388

Abstract

Designing good error correcting codes whose generator matrix has a support constraint, i.e., one for which only certain entries of the generator matrix are allowed to be nonzero, has found many recent applications, including in distributed coding and storage, linear network coding, multiple access networks, and weakly secure data exchange. The dual problem, where the parity check matrix has a support constraint, comes up in the design of locally repairable codes. The central problem here is to design codes with the largest possible minimum distance, subject to the given support constraint on the generator matrix. When the distance metric is the Hamming distance, the codes of interest are Reed-Solomon codes, for which case, the problem was formulated as the "GM-MDS conjecture." In the rank metric case, the same problem can be considered for Gabidulin codes. This thesis provides solutions to these problems and discusses the remaining open problems.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Linear codes; minimum distance; Reed–Solomon codes; Gabidulin codes; rank distance; network coding; distributed codes; distributed systems;
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Hassibi, Babak
Thesis Committee:
  • Kostina, Victoria (chair)
  • Bruck, Jehoshua
  • Umans, Christopher M.
  • Hassibi, Babak
Defense Date:1 December 2020
Record Number:CaltechTHESIS:05242021-223430388
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:05242021-223430388
DOI:10.7907/qz6m-wp22
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ISIT.2018.8437308DOIArticle adapted for Chapter 1.
https://doi.org/10.1109/ITW.2018.8613535DOIArticle adapted for Chapter 1.
https://doi.org/10.1109/TIT.2019.2932663DOIArticle adapted for Chapter 1.
https://doi.org/10.1109/ITW44776.2019.8988992DOIArticle adapted for Chapter 2.
https://doi.org/10.1109/TIT.2019.2955106DOIArticle adapted for Chapter 2.
https://doi.org/10.1109/ISIT44484.2020.9174524DOIArticle adapted for Chapter 3.
ORCID:
AuthorORCID
Yildiz, Hikmet0000-0002-0891-3352
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14172
Collection:CaltechTHESIS
Deposited By: Hikmet Yildiz
Deposited On:27 May 2021 15:44
Last Modified:03 Jun 2021 15:52

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