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The application of invariant theory to the existence of quasi-symmetric designs

Publication ,  Journal Article
Calderbank, AR
Published in: Journal of Combinatorial Theory, Series A
January 1, 1987

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.

Duke Scholars

Published In

Journal of Combinatorial Theory, Series A

DOI

EISSN

1096-0899

ISSN

0097-3165

Publication Date

January 1, 1987

Volume

44

Issue

1

Start / End Page

94 / 109

Related Subject Headings

  • Computation Theory & Mathematics
  • 0101 Pure Mathematics
 

Citation

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Calderbank, A. R. (1987). The application of invariant theory to the existence of quasi-symmetric designs. Journal of Combinatorial Theory, Series A, 44(1), 94–109. https://doi.org/10.1016/0097-3165(87)90062-8
Calderbank, A. R. “The application of invariant theory to the existence of quasi-symmetric designs.” Journal of Combinatorial Theory, Series A 44, no. 1 (January 1, 1987): 94–109. https://doi.org/10.1016/0097-3165(87)90062-8.
Calderbank AR. The application of invariant theory to the existence of quasi-symmetric designs. Journal of Combinatorial Theory, Series A. 1987 Jan 1;44(1):94–109.
Calderbank, A. R. “The application of invariant theory to the existence of quasi-symmetric designs.” Journal of Combinatorial Theory, Series A, vol. 44, no. 1, Jan. 1987, pp. 94–109. Scopus, doi:10.1016/0097-3165(87)90062-8.
Calderbank AR. The application of invariant theory to the existence of quasi-symmetric designs. Journal of Combinatorial Theory, Series A. 1987 Jan 1;44(1):94–109.
Journal cover image

Published In

Journal of Combinatorial Theory, Series A

DOI

EISSN

1096-0899

ISSN

0097-3165

Publication Date

January 1, 1987

Volume

44

Issue

1

Start / End Page

94 / 109

Related Subject Headings

  • Computation Theory & Mathematics
  • 0101 Pure Mathematics