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

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arxiv math/0612740 v1 pith:FFEDNK3C submitted 2006-12-23 math.CO

Hajime Tanaka This is my paper · ORCID
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keywords algebraapproachassmus-mattsonterwilligertheoremanotherbounddistance
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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.

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  1. The Lie algebra $\mathfrak{sl}_4(\mathbb C)$ and the hypercubes

    math.CO 2025-05 conditional novelty 7.0 of 10

    The degree-N polynomials in four variables, the fixed 3-tensors of the hypercube, and the hypercube Terwilliger algebra are all isomorphic as sl4(C)-modules, with explicit maps.

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