Skip to main content
SpringerLink
Log in

An algorithm for optimal difference systems of sets

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

Difference Systems of Sets (DSS) are combinatorial structures that generalize cyclic difference sets and are used in code synchronization. A DSS is optimal if the associated code has minimum redundancy for the given block length n, alphabet size q, and error-correcting capacity ρ. An algorithm for finding optimal DSS is presented together with tables of optimal solutions found by this algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Crick HC, Griffith JS, Orgel LE (1957) Codes without commas. Proc Nat Acad Sci 43:416–421

    Article  Google Scholar 

  • Cumming LJ (to appear) A family of circular systematic comma-free codes

  • Golomb SW, Gordon B, Welch LR (1958) Comma-free code. Can J Math 10(2):202–209

    MATH  Google Scholar 

  • Hall M Jr (1986) Combinatorial theory, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Kreher DL, Stinson DR (1998) Combinatorial algorithms: generation, enumeration, and search. CRC Press, Boca Raton

  • Levenshtein VI (1971) One method of constructing quasilinear codes providing synchronization in the presence of errors. Probl Inf Transm 7(3):215–222

    Google Scholar 

  • Levenshtein VI (2004) Combinatorial problems motivated by comma-free codes. J Comb Des 12(3):184–196

    Article  MATH  Google Scholar 

  • Mutoh Y, Tonchev VD (to appear) Difference systems of sets and cyclotomy. Discret Math

  • Tonchev VD (2003) Difference systems of sets and code synchronization. Rend Sem Mat Messina Ser II 9:217–226

    Google Scholar 

  • Tonchev VD (2005) Partitions of difference sets and code synchronization. Finite Fields Appl 11:601–621

    Article  MATH  Google Scholar 

  • Wang H (2006) A new bound for difference systems of sets. J Comb Math Comb Comput 58:161–168

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931-1295, USA

    Vladimir D. Tonchev & Hao Wang

Authors
  1. Vladimir D. Tonchev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir D. Tonchev.

Additional information

Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday.

Research supported by NSF Grant CCR-0310632.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tonchev, V.D., Wang, H. An algorithm for optimal difference systems of sets. J Comb Optim 14, 165–175 (2007). https://doi.org/10.1007/s10878-007-9064-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-007-9064-6

Keywords

Search

Navigation