• conflict-avoiding codes;
  • equi-difference;
  • optimal codes


For a k-subset X of inline image, the set of differences on X is the set inline image (mod n): inline image . A conflict-avoiding code CAC of length n and weight k is a collection inline image of k-subsets of inline image such that inline image = ∅ for any distinct inline image. Let CAC(inline image) be the class of all the CACs of length n and weight k. The maximum size of codes in CAC(n, k) is denoted by inline image. A code inline image CAC(n, k) is said to be optimal if inline image = inline image. An optimal code inline image is tight equi-difference if inline image = inline image and each codeword in inline image is of the form inline image. In this paper, the necessary and sufficient conditions for the existence problem of optimal tight equi-difference conflict-avoiding codes of length n = inline image and weight 3 are given. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 21: 223–231, 2013