Constructions for generalized Steiner systems GS(3, 4, v, 2)

Authors:
Haitao Cao;Lijun Ji;Lie Zhu
Affiliations:
Institute of Mathematics, School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing, China 210097;Department of Mathematics, Suzhou University, Suzhou, China 215006;Department of Mathematics, Suzhou University, Suzhou, China 215006
Venue:
Designs, Codes and Cryptography
Year:
2007

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Abstract

Generalized Steiner systems GS (3, 4, v, 2) were first discussed by Etzion and used to construct optimal constant weight codes over an alphabet of size three with minimum Hamming distance three, in which each codeword has length v and weight four. Not much is known for GS (3, 4, v, 2)s except for a recursive construction and two small designs for v = 8,10 given by Etzion. In this paper, more small designs are found by computer search and also given are direct constructions based on finite fields and rotational Steiner quadruple systems and recursive constructions using three-wise balanced designs. Some infinite families are also obtained.