Let v and k be positive integers. A (v, k, 1)-packing design is an ordered pair (V, B B B) where V is a v-set and B B B is a collection of k-subsets of V (called blocks) such that every 2-subset of V occurs in at most one block of B B B. The packing problem is mainly to determine the packing number
A General Construction for Optimal Cyclic Packing Designs
โ Scribed by Jianxing Yin
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 118 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0097-3165
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โฆ Synopsis
Cyclic packing designs of pairs have various applications in communications. In this paper, the concept of a (g 1 , g 2 , ..., g r ; u)-regular cyclic packing design is defined, and used to establish a quite general recursive construction concerning cyclic packing designs. As corollaries, we are able to unify many known constructions for cyclic designs. As an application, we obtain infinite series of new optimal cyclic packing designs which can be utilized directly to produce new optimal optical orthogonal codes.
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Corresponding to each odd integer q, we construct a complex orthogonal design. The number of variables and the form of the design depends on the integer q. Almost all of these designs are new and as a corollary we get a new asymptotic existence result for complex Hadamard matrices.