A relation between sequences generated by Golomb’s preference algorithm

In a recent paper (DCC, Rubin and Weiss in 85:547–555, 2017), based on the differentiation operator, Rubin and Weiss proposed 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 . Both prefer-opposite and prefer-one de Br...

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Bibliographic Details
Published inDesigns, codes, and cryptography Vol. 91; no. 1; pp. 285 - 291
Main Author Jiang, Yupeng
Format Journal Article
LanguageEnglish
Published New York Springer US 01.01.2023
Springer Nature B.V
Subjects
Algorithms
Boolean
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Sequences
Prefer-one sequence
Inertia function
94A55
Preference function
68W32
68R15
Online AccessGet full text
ISSN0925-1022
1573-7586
DOI10.1007/s10623-022-01108-1

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Summary:In a recent paper (DCC, Rubin and Weiss in 85:547–555, 2017), based on the differentiation operator, Rubin and Weiss proposed 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 . Both prefer-opposite and prefer-one de Bruijn sequences can be regarded as special cases of sequences generated by Golomb’s preference algorithm. In this paper, we introduce inertia function in Golomb’s preference algorithm, and then applying it to extend Rubin and Weiss’s result to more general cases.
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ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-022-01108-1