## 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(⟨ b_{1}, … , b_{l}⟩) = ⟨ b_{2}- b_{1}, b_{3}- b_{2}, … , b_{l}- b_{l} _{-} _{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 language | English |
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Pages (from-to) | 547-555 |

Number of pages | 9 |

Journal | Designs, Codes, and Cryptography |

Volume | 85 |

Issue number | 3 |

DOIs | |

State | Published - 1 Dec 2017 |

## Keywords

- De Bruijn sequences
- Prefer one
- Prefer opposite

## ASJC Scopus subject areas

- Computer Science Applications
- Applied Mathematics