Explicit Hermitian self-dual MDS codes prove the existence of AME(12,5), AME(18,11), AME(18,13) and the projections AME(17,11), AME(17,13).
New MDS Euclidean and Hermitian self-dual codes over finite fields
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abstract
In this paper, we construct MDS Euclidean self-dual codes which are extended cyclic duadic codes. And we obtain many new MDS Euclidean self-dual codes. We also construct MDS Hermitian self-dual codes from generalized Reed-Solomon codes and constacyclic codes. And we give some results on Hermitian self-dual codes, which are the extended cyclic duadic codes.
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Symmetry-guided constructions of absolutely maximally entangled states in five open cases
Explicit Hermitian self-dual MDS codes prove the existence of AME(12,5), AME(18,11), AME(18,13) and the projections AME(17,11), AME(17,13).