Stretching de Bruijn sequences

We give a one-step construction of de Bruijn sequences of general alphabet size and with order n + k , given a de Bruijn sequence of order n and any integer k > 1 . This is achieved by using an appropriate class of graph homomorphisms between de Bruijn digraphs whose orders differ by an integer k...

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Bibliographic Details
Published inDesigns, codes, and cryptography Vol. 85; no. 2; pp. 381 - 394
Main Authors Alhakim, Abbas, Nouiehed, Maher
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2017
Springer Nature B.V
Subjects
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Graph theory
Homomorphisms
Information and Communication
Sequences
Stretching
05C45
68R01
de Bruijn sequence
05C60
Recursive construction
Linear feedback shift register
de Bruijn graph homomorphism
Lempel’s D-morphism
05C38
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Summary:We give a one-step construction of de Bruijn sequences of general alphabet size and with order n + k , given a de Bruijn sequence of order n and any integer k > 1 . This is achieved by using an appropriate class of graph homomorphisms between de Bruijn digraphs whose orders differ by an integer k . The method starts with a lower order de Bruijn cycle, finds its inverse cycles in the higher order digraph, which are then cross-joined into one full cycle. Therefore, this generalizes the Lempel’s binary construction and the Alhakim–Akinwande construction for non-binary alphabets and a wide class of homomorphisms.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-016-0314-4