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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| Published in | Designs, codes, and cryptography Vol. 91; no. 1; pp. 285 - 291 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.01.2023
Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 0925-1022 1573-7586 |
| DOI | 10.1007/s10623-022-01108-1 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Jiang, Yupeng |
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| Cites_doi | 10.1007/s10623-016-0314-4 10.1137/1024041 10.1016/S0019-9958(79)90708-3 10.1016/j.dam.2011.11.024 10.1090/S0002-9904-1934-05988-3 10.1007/s10623-016-0322-4 10.4169/000298910x515794 10.1007/s00200-020-00459-3 |
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| Copyright | The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. |
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| References | Mandal, Gong, Knudsen, Wu (CR9) 2012 Solomon (CR13) 1967 Alhakim (CR3) 2012; 160 CR6 CR5 Martin (CR10) 1934; 40 CR14 Alhakim (CR2) 2010; 117 Abraham (CR1) 1970; 19 Green, Dimond (CR8) 1970; 117 Alhakim, Nouiehed (CR4) 2017; 85 Fredricksen (CR7) 1982; 24 Mykkeltveit, Siu, Tong (CR11) 1979; 43 Rubin, Weiss (CR12) 2017; 85 1108_CR6 K Mandal (1108_CR9) 2012 AM Alhakim (1108_CR2) 2010; 117 MH Martin (1108_CR10) 1934; 40 A Rubin (1108_CR12) 2017; 85 H Fredricksen (1108_CR7) 1982; 24 1108_CR14 A Alhakim (1108_CR3) 2012; 160 DH Green (1108_CR8) 1970; 117 W Solomon (1108_CR13) 1967 L Abraham (1108_CR1) 1970; 19 A Alhakim (1108_CR4) 2017; 85 J Mykkeltveit (1108_CR11) 1979; 43 1108_CR5 |
| References_xml | – volume: 85 start-page: 381 year: 2017 end-page: 394 ident: CR4 article-title: Stretching de bruijn sequences publication-title: Des. Codes Crypt. doi: 10.1007/s10623-016-0314-4 – volume: 24 start-page: 195 issue: 2 year: 1982 end-page: 221 ident: CR7 article-title: A survey of full length nonlinear shift register cycle algorithms publication-title: SIAM Rev. doi: 10.1137/1024041 – volume: 43 start-page: 202 issue: 2 year: 1979 end-page: 215 ident: CR11 article-title: On the cycle structure of some nonlinear shift register sequences publication-title: Inf. Control doi: 10.1016/S0019-9958(79)90708-3 – volume: 117 start-page: 681 issue: 4 year: 1970 end-page: 686 ident: CR8 article-title: Nonlinear product-feedback shift registers publication-title: Proc. IEE – ident: CR14 – volume: 19 start-page: 1204 issue: 12 year: 1970 end-page: 1209 ident: CR1 article-title: On a homomorphism of the de bruijn graph and its applications to the design of feedback shift registers publication-title: IEEE Trans. Comput. C – start-page: 104 year: 2012 end-page: 118 ident: CR9 article-title: Cryptographically strong de bruijn sequences with large periods publication-title: Selected Areas in Cryptography, SAC 2012 – volume: 160 start-page: 992 issue: 7 year: 2012 end-page: 998 ident: CR3 article-title: Spans of preference functions for de bruijn sequences publication-title: Discret. Appl. Math. doi: 10.1016/j.dam.2011.11.024 – volume: 40 start-page: 859 issue: 12 year: 1934 end-page: 864 ident: CR10 article-title: A problem in arrangements publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0002-9904-1934-05988-3 – volume: 85 start-page: 547 year: 2017 end-page: 555 ident: CR12 article-title: Mapping prefer-opposite to prefer-one de bruijn sequences publication-title: Des. Codes Crypt. doi: 10.1007/s10623-016-0322-4 – ident: CR6 – volume: 117 start-page: 728 year: 2010 end-page: 732 ident: CR2 article-title: A simple combinatorial algorithm for de bruijn sequences publication-title: Am. Math. Mon. doi: 10.4169/000298910x515794 – ident: CR5 – year: 1967 ident: CR13 publication-title: Golomb – volume: 160 start-page: 992 issue: 7 year: 2012 ident: 1108_CR3 publication-title: Discret. Appl. Math. doi: 10.1016/j.dam.2011.11.024 – ident: 1108_CR6 doi: 10.1007/s00200-020-00459-3 – volume: 85 start-page: 547 year: 2017 ident: 1108_CR12 publication-title: Des. Codes Crypt. doi: 10.1007/s10623-016-0322-4 – volume: 117 start-page: 728 year: 2010 ident: 1108_CR2 publication-title: Am. Math. Mon. doi: 10.4169/000298910x515794 – volume: 24 start-page: 195 issue: 2 year: 1982 ident: 1108_CR7 publication-title: SIAM Rev. doi: 10.1137/1024041 – start-page: 104 volume-title: Selected Areas in Cryptography, SAC 2012 year: 2012 ident: 1108_CR9 – volume: 19 start-page: 1204 issue: 12 year: 1970 ident: 1108_CR1 publication-title: IEEE Trans. Comput. C – volume: 85 start-page: 381 year: 2017 ident: 1108_CR4 publication-title: Des. Codes Crypt. doi: 10.1007/s10623-016-0314-4 – volume-title: Golomb year: 1967 ident: 1108_CR13 – ident: 1108_CR5 doi: 10.1007/s00200-020-00459-3 – volume: 117 start-page: 681 issue: 4 year: 1970 ident: 1108_CR8 publication-title: Proc. IEE – volume: 43 start-page: 202 issue: 2 year: 1979 ident: 1108_CR11 publication-title: Inf. Control doi: 10.1016/S0019-9958(79)90708-3 – volume: 40 start-page: 859 issue: 12 year: 1934 ident: 1108_CR10 publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0002-9904-1934-05988-3 – ident: 1108_CR14 |
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| SubjectTerms | Algorithms Boolean Coding and Information Theory Computer Science Cryptology Discrete Mathematics in Computer Science Sequences |
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| Title | A relation between sequences generated by Golomb’s preference algorithm |
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