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.
New proofs of the Assmus-Mattson theorem based on the Terwilliger algebra
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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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The Lie algebra $\mathfrak{sl}_4(\mathbb C)$ and the hypercubes
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.