The extended binary quadratic residue code of length 42 holds a 3−design

Alexis Bonnecaze (1) , Patrick Solé (1)

1 I2M - Institut de Mathématiques de Marseille

The codewords of weight 10 of the [42, 21, 10] extended binary quadratic residue code are shown to hold a design of parameters 3 − (42, 10, 18). Its automorphism group is isomorphic to P SL(2, 41). Its existence can be explained neither by a transitivity argument, nor by the Assmus-Mattson theorem.

Mots clés: designs; quadratic residue codes; Assmus-Mattson theorem

Domaines: Mathématiques [math]

Alexis Bonnecaze, Patrick Solé. The extended binary quadratic residue code of length 42 holds a 3−design. Journal of Combinatorial Designs, 2021. ⟨hal-03217485⟩