Designs and Representation of the Symmetric Group

  • Authors:

  • David Masson

  • Affiliations:

  • Laboratoire d'Algorithmique Arithmétique, 351 Cours de la Libération, 33405 Talence, France masson@math.u-bordeaux.fr

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2003

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Abstract

We study (generalized) designs supported by words of given composition. We characterize them in terms of orthogonality relations with Specht modules; we define some zonal functions for the symmetric group and we give a closed formula for them, indexed on ordered pair of semi-standard generalized tableaux: Hahn polynomials are a particular case. We derive an algorithm to test if a set \mathcal{B} is a design. We use it to search designs in some ternary self-dual codes.