engleski

Quasi-symmetric 2-(64, 24, 46) designs derived from AG(3, 4)

In this talk we present the enumeration of quasi-symmetric 2-(64, 24, 46) designs supported by the dual code C? of the binary linear code C spanned by the lines of AG(3, 4). It is shown that C? supports exactly 30, 264 nonisomorphic quasi-symmetric 2-(64, 24, 46) designs. The block graph of a quasi-symmetric 2- (64, 24, 46) design with block intersection numbers 8 and 12, where two blocks are adjacent if they share 12 points, is a strongly regular graph with parameters (336, 80, 28, 16). The block graphs of the 2699 nonisomorphic quasi- symmetric 2-(64, 24, 46) designs admitting an automorphism of order 128, split into 2371 isomorphism classes of strongly regular graphs with parameters (336, 80, 28, 16). The automorphism groups of those strongly regular graphs are computed.

quasi-symmetric design

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