Optimal conflict-avoiding codes of length n ≡ 0 (mod 16) and weight 3

Miwako Mishima*, Hung-Lin Fu, Shoichi Uruno

*Corresponding author for this work

Research output: Contribution to journalArticle

30 Scopus citations

Abstract

A conflict-avoiding code of length n and weight k is defined as a set C ⊆ {0, 1}n of binary vectors, called codewords, all of Hamming weight k such that the distance of arbitrary cyclic shifts of two distinct codewords in C is at least 2k-2. In this paper, we obtain direct constructions for optimal conflict-avoiding codes of length n = 16m and weight 3 for any m by utilizing Skolem type sequences. We also show that for the case n = 16m + 8 Skolem type sequences can give more concise constructions than the ones obtained earlier by Jimbo et al.

Original languageEnglish
Pages (from-to)275-291
Number of pages17
JournalDesigns, Codes, and Cryptography
Volume52
Issue number3
DOIs
StatePublished - 1 Sep 2009

Keywords

  • Conflict-avoiding codes
  • Extended Langford sequences
  • Extended Skolem sequences
  • Near-Skolem sequences

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