Maximum Length of Robust Positioning Sequences

Duc Tu Dao, Han Mao Kiah, Hengjia Wei

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


An (n,d)-robust positioning sequence (RPS) is a binary sequence where every pair of length-n subwords is distance d apart. In this paper, we study the quantity P(n,d), which denotes maximum length of an (n,d)-RPS, and provide tight estimates in the range n/2 < d ≤ n. First, we show that the usual Plotkin bound cannot be attained when certain divisibility conditions hold. Next, using the concept of differences, we construct an infinite family of RPSs that attain a modified Plotkin bound. Finally, except for 16 cases, we determine the exact values of P(n,d) for δ(n) ≤ d ≤ n ≤ 50, where δ(n) = ⌈n/2⌉ if n ≢ 0(mod 4) and δ(n) = (n +2)/2 if n ≡ 0(mod 4).

Original languageEnglish
Title of host publication2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers
Number of pages6
ISBN (Electronic)9781728164328
StatePublished - 1 Jun 2020
Event2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States
Duration: 21 Jul 202026 Jul 2020

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Conference2020 IEEE International Symposium on Information Theory, ISIT 2020
Country/TerritoryUnited States
CityLos Angeles

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics


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