Optimal grid holey packings with block size 3 and 4

  • Authors:

  • Bin Wen;Jianmin Wang;Jianxing Yin

  • Affiliations:

  • Department of Mathematics, Suzhou University, Suzhou, People's Republic of China 215006 and Department of Mathematics, Changshu Institute of Technology, Suzhou, People's Republic of China 215500;Department of Mathematics, Suzhou University, Suzhou, People's Republic of China 215006;Department of Mathematics, Suzhou University, Suzhou, People's Republic of China 215006

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2009

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Abstract

The notion of a grid holey packing (GHP) was first proposed for the construction of constant composite codes. For a GHP (k, 1; n 脳 g) of type [w 1, . . . , w g ], where $${k = \sum_{j=1}^{g} w_j}$$ , the fundamental problem is to determine the packing number N([w 1, . . . , w g ], 1; n 脳 g), that is, the maximum number of blocks in such a GHP. In this paper we determine completely the values of N([w 1, . . . , w g ], 1; n 脳 g) in the case of block size $${k\in \{3, 4\}}$$ .