Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors

Hengjia Wei, Moshe Schwartz

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error ball. We construct two classes of such perfect codes correcting a single burst of length 2, where each error affects the corresponding position by increasing it by one, both for cyclic and non-cyclic bursts. We also present a generic construction that requires a primitive element in a finite field with specific properties. We then show that in various parameter regimes such primitive elements exist, and hence, infinitely many perfect burst-correcting codes exist.

Original languageEnglish
Pages (from-to)951-962
Number of pages12
JournalIEEE Transactions on Information Theory
Volume69
Issue number2
DOIs
StatePublished - 1 Feb 2023

Keywords

  • Integer coding
  • burst-correcting codes
  • lattices
  • limited-magnitude errors
  • perfect codes

ASJC Scopus subject areas

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

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