Designs and self-dual codes with long shadows

  • Authors:
  • Christine Bachoc;Philippe Gaborit

  • Affiliations:
  • Laboratoire A2X, Université Bordeaux I, 351, Cours de la Libération, 33405 Talence, France;LACO, Université de Limoges, 123, av A. Thomas, 87000 Limoges, France

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2004

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Abstract

In this paper we introduce the notion of s-extremal codes for self-dual binary codes and we relate this notion to the existence of 1-designs or 2-designs in these codes. We extend the classification of codes with long shadows of Elkies (Math. Res. Lett. 2(5) (1995) 643) to codes with minimum distance 6, for which we give partial classification.