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Toric Varieties and Codes, Error-correcting Codes, Quantum Codes, Secret Sharing and Decoding

08/20/2018

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by Johan P. Hansen, et al.

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We present toric varieties and associated toric codes and their decoding. Toric codes are applied to construct Linear Secret Sharing Schemes (LSSS) with strong multiplication by the Massey construction. Asymmetric Quantum Codes are obtained from toric codes by the A.R. Calderbank P.W. Shor and A.M. Steane construction of stabilizer codes (CSS) from linear codes containing their dual codes.

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