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

Hikmet Yildiz, Babak Hassibi

Research output: Contribution to journalArticlepeer-review

1 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

ASJC Scopus subject areas

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

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