Mapping prefer-opposite to prefer-one de Bruijn sequences

Amir Rubin, Gera Weiss

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We present a mapping of the binary prefer-opposite de Bruijn sequence of order n onto the binary prefer-one de Bruijn sequence of order n- 1. The mapping is based on the differentiation operator D(⟨ b1, … , bl⟩) = ⟨ b2- b1, b3- b2, … , bl- bl - 1⟩ where bit subtraction is modulo two. We show that if we take the prefer-opposite sequence ⟨b1,b2,…,b2n⟩, apply D to get the sequence ⟨b^1,…,b^2n-1⟩ and drop all the bits b^ i such that ⟨ b^ i, … , b^ i + n - 1⟩ is a substring of ⟨ b^ 1, … , b^ i + n - 2⟩ , we get the prefer-one de Bruijn sequence of order n- 1.

Original languageEnglish
Pages (from-to)547-555
Number of pages9
JournalDesigns, Codes, and Cryptography
Volume85
Issue number3
DOIs
StatePublished - 1 Dec 2017

Keywords

  • De Bruijn sequences
  • Prefer one
  • Prefer opposite

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