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Designs, Codes and Cryptography

, Volume 52, Issue 1, pp 107–124 | Cite as

Optimal grid holey packings with block size 3 and 4

  • Bin Wen
  • Jianmin Wang
  • Jianxing Yin
Article

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 ×  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 ×  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 ×  g) in the case of block size \({k\in \{3, 4\}}\) .

Keywords

Grid holey packing Optimal Segmental grid holey packing 

Mathematics Subject Classification (2000)

05B30 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsSuzhou UniversitySuzhouPeople’s Republic of China
  2. 2.Department of MathematicsChangshu Institute of TechnologySuzhouPeople’s Republic of China

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