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

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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.
OriginalsprogEngelsk
TidsskriftarXiv
StatusUdgivet - 20 aug. 2018
Begivenhed CIMPA School: Commutative Algebra and applications to Coding Theory and Algebraic Statistics. - Mexico
Varighed: 15 jun. 201815 jul. 2018

Konference

Konference CIMPA School: Commutative Algebra and applications to Coding Theory and Algebraic Statistics.
LokationMexico
Periode15/06/201815/07/2018

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