New proofs of the Assmus-Mattson theorem based on the Terwilliger algebra

Abstract

We use the Terwilliger algebra to provide a new approach to the Assmus-Mattson theorem. This approach also includes another proof of the minimum distance bound shown by Martin as well as its dual.

15 pages

References in corpus (1)

• Some algebra related to $P$-and $Q$-polynomial association schemes

Cited by in corpus (9)

• Distance-regular graphs
• Commutative association schemes
• On relative $t$-designs in polynomial association schemes
• Nonsymmetric Askey-Wilson polynomials and $Q$-polynomial distance-regular graphs
• On the shape of a tridiagonal pair
• An Assmus-Mattson theorem for codes over commutative association schemes
• Vertex subsets with minimal width and dual width in $Q$-polynomial distance-regular graphs
• Semidefinite programming bounds for error-correcting codes
• Tight relative $t$-designs on two shells in hypercubes, and Hahn and Hermite polynomials