Cyclic Difference Packing and Covering Arrays

  • Authors:

  • Jianxing Yin

  • Affiliations:

  • Department of Mathematics, Suzhou University, Suzhou, China 215006

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2005

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Abstract

Let n and k be positive integers. Let Cq be a cyclic group of order q. A cyclic difference packing (covering) array, or a CDPA(k, n; q) (CDCA(k, n; q)), is a k 脳 n array (aij) with entries aij (0 驴 i 驴 k驴1, 0 驴 j 驴 n驴1) from Cq such that, for any two rows t and h (0 驴 t h 驴 k驴1), every element of Cq occurs in the difference list $${\Delta}_{th} = {d_{hj}- d_{tj}: j = 0, 1, \dots, n-1}$$ at most (at least) once. When q is even, then n 驴 q驴1 if a CDPA(k, n; q) with k 驴 3 exists, and n 驴 q+1 if a CDCA(k, n; q) with k 驴 3 exists. It is proved that a CDCA(4, q+1; q) exists for any even positive integers, and so does a CDPA(4, q驴1; q) or a CDPA(4, q驴2; q). The result is established, for the most part, by means of a result on cyclic difference matrices with one hole, which is of interest in its own right.