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The first construction of strongly secure quantum ramp secret sharing byZhang and Matsumoto had an undesirable feature that the dimension of quantumshares must be larger than the number of shares. By using algebraic curves overfinite fields, we propose a new construction in which the number of shares canbecome arbitrarily large for fixed dimension of shares.

Strongly Secure Quantum Ramp Secret Sharing Constructed from Algebraic Curves over Finite Fields