Conflict-avoiding codes and cyclic triple systems

Conflict-avoiding codes and cyclic triple systems The paper deals with the problem of constructing a code of the maximum possible cardinality consisting of binary vectors of length n and Hamming weight 3 and having the following property: any 3 × n matrix whose rows are cyclic shifts of three different code vectors contains a 3 × 3 permutation matrix as a submatrix. This property (in the special case w = 3) characterizes conflict-avoiding codes of length n for w active users, introduced in [1]. Using such codes in channels with asynchronous multiple access allows each of w active users to transmit a data packet successfully in one of w attempts during n time slots without collisions with other active users. An upper bound on the maximum cardinality of a conflict-avoiding code of length n with w = 3 is proved, and constructions of optimal codes achieving this bound are given. In particular, there are found conflict-avoiding codes for w = 3 which have much more vectors than codes of the same length obtained from cyclic Steiner triple systems by choosing a representative in each cyclic class. Problems of Information Transmission Springer Journals

Conflict-avoiding codes and cyclic triple systems

Loading next page...
Copyright © 2007 by Pleiades Publishing, Inc.
Engineering; Communications Engineering, Networks; Electronic and Computer Engineering; Information Storage and Retrieval; Systems Theory, Control
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial