Math @ Duke
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Publications [#236011] of Robert Calderbank
Papers Published
- Calderbank, AR, The application of invariant theory to the existence of quasi-symmetric designs,
Journal of Combinatorial Theory, Series A, vol. 44 no. 1
(January, 1987),
pp. 94-109, Elsevier BV, ISSN 0097-3165 [doi]
(last updated on 2024/03/28)
Abstract: Gleason and Mallows and Sloane characterized the weight enumerators of maximal self-orthogonal 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). Non-existence of quasi-symmetric 2-(21, 18, 14), 2-(21, 9, 12), and 2-(35, 7, 3) designs follows directly from the theorem. We also eliminate quasi-symmetric 2-(33, 9, 6) designs. We prove that the blocks of quasi-symmetric 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 quasi-symmetric 2-(19,9, 16) and 2-(22, 8, 12) designs. © 1987.
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