5 citations · 20 across the 10 of their papers we have counts for
10 papers
Toric Varieties and Codes, Error-correcting Codes, Quantum Codes, Secret Sharing and Decoding
Johan P. Hansen
Toric varieties and their associated toric codes, as well as determination of their parameters with intersection theory, are presented in the two dimensional case. Linear Secret Sh…
Asymmetric Quantum Codes on Toric Surfaces
Johan P. Hansen
Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubit-flip and phase-shift errors may have equal or different probabilities. The c…
Toric Codes, Multiplicative Structure and Decoding
Johan P. Hansen
Long linear codes constructed from toric varieties over finite fields, their multiplicative structure and decoding. The main theme is the inherent multiplicative structure on toric…
Riemann-Roch Spaces and Linear Network Codes
Johan P. Hansen
We construct linear network codes utilizing algebraic curves over finite fields and certain associated Riemann-Roch spaces and present methods to obtain their parameters. In partic…
Secret Sharing Schemes with a large number of players from Toric Varieties
Johan P. Hansen
A general theory for constructing linear secret sharing schemes over a finite field $\Fq$ from toric varieties is introduced. The number of players can be as large as f…
Forms and Linear Network Codes
Johan P. Hansen
We present a general theory to obtain linear network codes utilizing forms and obtain explicit families of equidimensional vector spaces, in which any pair of distinct vector space…