15 citations · 23 across the 7 of their papers we have counts for
17 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…
Twisted Reed-Solomon Codes
Peter Beelen, Sven Puchinger, Johan Rosenkilde
In this article, we present a new construction of evaluation codes in the Hamming metric, which we call twisted Reed-Solomon codes. Whereas Reed-Solomon (RS) codes are MDS codes, t…
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…
Bounds on List Decoding of Linearized Reed-Solomon Codes
Sven Puchinger, Johan Rosenkilde
Linearized Reed-Solomon (LRS) codes are sum-rank metric codes that fulfill the Singleton bound with equality. In the two extreme cases of the sum-rank metric, they coincide with Re…
Decoding of Interleaved Alternant Codes
Lukas Holzbaur, Hedongliang Liu, Alessandro Neri +4
Interleaved Reed-Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a…
Fast Decoding of Codes in the Rank, Subspace, and Sum-Rank Metric
Hannes Bartz, Thomas Jerkovits, Sven Puchinger +1
We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the subs…
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…
Generic Decoding in the Sum-Rank Metric
Sven Puchinger, Julian Renner, Johan Rosenkilde
We propose the first non-trivial generic decoding algorithm for codes in the sum-rank metric. The new method combines ideas of well-known generic decoders in the Hamming and rank m…
Verification Protocols with Sub-Linear Communication for Polynomial Matrix Operations
David Lucas, Vincent Neiger, Clément Pernet +2
We design and analyze new protocols to verify the correctness of various computations on matrices over the ring F[x] of univariate polynomials over a field F. For the sake of effic…
Computing Popov and Hermite forms of rectangular polynomial matrices
Vincent Neiger, Johan Rosenkilde, Grigory Solomatov
We consider the computation of two normal forms for matrices over the univariate polynomials: the Popov form and the Hermite form. For matrices which are square and nonsingular, de…
Improved Power Decoding of Interleaved One-Point Hermitian Codes
Sven Puchinger, Johan Rosenkilde, Irene Bouw
We propose a new partial decoding algorithm for -interleaved one-point Hermitian codes that can decode-under certain assumptions-an error of relative weight up to $1-(\tfrac{k+g…
Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography
Peter Beelen, Martin Bossert, Sven Puchinger +1
We present a generalisation of Twisted Reed-Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under du…
Two-Point Codes for the Generalized GK curve
Elise Barelli, Peter Beelen, Mrinmoy Datta +2
We improve previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti-Korchmaros curve (GGK). Castellanos and Ti…
Fast Computation of the Roots of Polynomials Over the Ring of Power Series
Vincent Neiger, Johan Rosenkilde, Eric Schost
We give an algorithm for computing all roots of polynomials over a univariate power series ring over an exact field . More precisely, given a precision , and a polyn…
Improved Power Decoding of One-Point Hermitian Codes
Sven Puchinger, Irene Bouw, Johan Rosenkilde né Nielsen
We propose a new partial decoding algorithm for one-point Hermitian codes that can decode up to the same number of errors as the Guruswami--Sudan decoder. Simulations suggest that…
Decoding of Interleaved Reed-Solomon Codes Using Improved Power Decoding
Sven Puchinger, Johan Rosenkilde né Nielsen
We propose a new partial decoding algorithm for -interleaved Reed--Solomon (IRS) codes that can decode, with high probability, a random error of relative weight $1-R^{\frac{m}{m…