4 papers
Fast Decoding of AG Codes
Peter Beelen, Johan Rosenkilde, Grigory Solomatov
We present an efficient list decoding algorithm in the style of Guruswami-Sudan for algebraic geometry codes. Our decoder can decode any such code using $\tilde{\mathcal O}(s\ell^ω…
Improved Power Decoding of Algebraic Geometry Codes
Sven Puchinger, Johan Rosenkilde, Grigory Solomatov
Power decoding is a partial decoding paradigm for arbitrary algebraic geometry codes for decoding beyond half the minimum distance, which usually returns the unique closest codewor…
Fast Encoding of AG Codes over Curves
Peter Beelen, Johan Rosenkilde, Grigory Solomatov
We investigate algorithms for encoding of one-point algebraic geometry (AG) codes over certain plane curves called curves, as well as algorithms for inverting the encoding…
Generic bivariate multi-point evaluation, interpolation and modular composition with precomputation
Vincent Neiger, Johan Rosenkilde, Grigory Solomatov
Suppose is a large enough field and is a fixed, generic set of points which is available for precomputation. We introduce a techniqu…