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The Implementation of Symplectic Matroids

What is symplectic matroids?

1998, A.V. Borvik, I.M. Gelfand, N. White construct the idea of special generization of matroid [1]. 1968, P. Sarvepalli found that the representation of symplectic matroids is parity check matrix of quantum code (stabilizer codes).

What can this notebook do?

  • To check the concrete example of concept appearing in the symplectic matroids and it's preliminary.
  • To find the nontrivial representable uniform symplectic matroids

In thesis [1], some admissible concept, and this notebook help you to understand the concept.

What is uniform symplectic matroids?

This is Analogy of uniform matroids. It is found in the process of my graduation research. The Base is made from a family of $k$ -admissible subsets of ground set $J$. I proved that using representation of uniform matroids $A$ and diagonal matrix D (with no 0 column vector), uniform symplectic matroids is represented by $(A \mid AD)$. However, I think there may be another representation and more generized method to represent.

References

[1] A.V. Borvik, I.M. Gelfand, N. White, Symplectic matroids, J. Algebraic Combin. 8 (1998), 235–252.

[2] D. Gale, Optimal assignments in an ordered set: An application of matroid theory, J. Combin. Theory 4 (1968), 176–180.