On the equivalence of certain constant weight codes and combinatorial designs |
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| Institution: | 1. University of Greifswald, Institute of Geography and Geology, Friedrich-Ludwig-Jahn-Str. 17a, 17487 Greifswald, Germany;2. Competence Center for Material Moisture (CMM) and Institute for Functional Interfaces (IFG), Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany;3. Leipzig University, Inst. of Experimental Physics II, Linnéstr. 5, 04103 Leipzig, Germany |
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| Abstract: | Stinson and van Rees (Combinatorica (1984), 357–362) proved that the existence of an equidistant code E: (n = 4s + 1,d = 2s, N) with N = n implies the existence of a certain symmetrical BIB design. This result is extended here for the constant weight codes with the same n and d. A theorem on the equivalence of a Hadamard matrix and a certain constant weight code is also proved. |
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