Math @ Duke

Publications [#236011] of Robert Calderbank
Papers Published
 Calderbank, AR, The application of invariant theory to the existence of quasisymmetric designs,
Journal of Combinatorial Theory, Series A, vol. 44 no. 1
(1987),
pp. 94109, ISSN 00973165
(last updated on 2018/07/22)
Abstract: Gleason and Mallows and Sloane characterized the weight enumerators of maximal selforthogonal codes with all weights divisible by 4. We apply these results to obtain a new necessary condition for the existence of 2  (v, k, λ) designs where the intersection numbers s1...,sn satisfy s1 ≡ s2 ≡ ... ≡ sn (mod 2). Nonexistence of quasisymmetric 2(21, 18, 14), 2(21, 9, 12), and 2(35, 7, 3) designs follows directly from the theorem. We also eliminate quasisymmetric 2(33, 9, 6) designs. We prove that the blocks of quasisymmetric 2(19, 9, 16), 2(20, 10, 18), 2(20,8, 14), and 2(22, 8, 12) designs are obtained from octads and dodecads in the [24, 12] Golay code. Finally we eliminate quasisymmetric 2(19,9, 16) and 2(22, 8, 12) designs. © 1987.


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