Optimum Linear Codes With Support-Constrained Generator Matrices Over Small Fields

Hikmet Yildiz, Babak Hassibi

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We consider the problem of designing optimal linear codes (in terms of having the largest minimum distance) subject to a support constraint on the generator matrix. We show that the largest minimum distance can be achieved by a subcode of a Reed-Solomon code of small field size and with the same minimum distance. In particular, if the code has length n , and maximum minimum distance d (over all generator matrices with the given support), then an optimal code exists for any field size q≥ 2n-d. As a by-product of this result, we settle the GM-MDS conjecture in the affirmative.
Original languageEnglish (US)
Pages (from-to)7868-7875
Number of pages8
JournalIEEE Transactions on Information Theory
Volume65
Issue number12
DOIs
StatePublished - Dec 2019
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2021-04-10
Acknowledgements: This work was supported in part by the National Science Foundation under Grant CNS-0932428, Grant CCF-1018927, Grant CCF1423663, and Grant CCF-1409204, in part by Qualcomm Inc., in part by the NASAs Jet Propulsion Laboratory through the President and Directors Fund, and in part by the King Abdullah University of Science and Technology
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

  • Library and Information Sciences
  • Information Systems
  • Computer Science Applications

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