Generalized Steiner systems GS4 (2, 4, v,g) for g = 2, 3, 6 |
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Authors: | D Wu G Ge L Zhu |
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Abstract: | Generalized Steiner systems GSd(t, k, v, g) were first introduced by Etzion and used to construct optimal constant‐weight codes over an alphabet of size g + 1 with minimum Hamming distance d, in which each codeword has length v and weight k. Much work has been done for the existence of generalized Steiner triple systems GS(2, 3, v, g). However, for block size four there is not much known on GSd(2, 4, v, g). In this paper, the necessary conditions for the existence of a GSd(t, k, v, g) are given, which answers an open problem of Etzion. Some singular indirect product constructions for GSd(2, k, v, g) are also presented. By using both recursive and direct constructions, it is proved that the necessary conditions for the existence of a GS4(2, 4, v, g) are also sufficient for g = 2, 3, 6. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 401–423, 2001 |
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Keywords: | generalized Steiner systems constant‐weight codes skew starter singular indirect product construction |
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