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Toric varieties and their associated toric codes, as well as determination oftheir parameters with intersection theory, are presented in the two dimensionalcase.  Linear Secret Sharing Schemes with strong multiplication are constructed fromtoric varieties and codes by the J. L. 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 fromlinear codes containing their dual codes.  Decoding of a class of toric codes is presented.

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