135 research outputs found
The Berlekamp-Massey Algorithm revisited
We propose a slight modification of the Berlekamp-Massey Algorithm for
obtaining the minimal polynomial of a given linearly recurrent sequence. Such a
modification enables to explain it in a simpler way and to adapt it to lazy
evaluation.Comment: in English and French version
Re-encoding reformulation and application to Welch-Berlekamp algorithm
The main decoding algorithms for Reed-Solomon codes are based on a bivariate
interpolation step, which is expensive in time complexity. Lot of interpolation
methods were proposed in order to decrease the complexity of this procedure,
but they stay still expensive. Then Koetter, Ma and Vardy proposed in 2010 a
technique, called re-encoding, which allows to reduce the practical running
time. However, this trick is only devoted for the Koetter interpolation
algorithm. We propose a reformulation of the re-encoding for any interpolation
methods. The assumption for this reformulation permits only to apply it to the
Welch-Berlekamp algorithm
Simple closed form Hankel transforms based on the central coefficients of certain Pascal-like triangles
We study the Hankel transforms of sequences related to the central
coefficients of a family of Pascal-like triangles. The mechanism of Riordan
arrays is used to elucidate the structure of these transforms
On interpolation-based decoding of a class of maximum rank distance codes
In this paper we present an interpolation-based decoding algorithm to decode a family of maximum rank distance codes proposed recently by Trombetti and Zhou. We employ the properties of the Dickson matrix associated with a linearized polynomial with a given rank and the modified Berlekamp-Massey algorithm in decoding. When the rank of the error vector attains the unique decoding radius, the problem is converted to solving a quadratic polynomial, which ensures that the proposed decoding algorithm has polynomial-time complexity.acceptedVersio
Galois theory, splitting fields and computer algebra
AbstractWe provide some algorithms for dynamically obtaining both a possible representation of the splitting field and the Galois group of a given separable polynomial from its universal decomposition algebra
Fuzzy Authentication using Rank Distance
Fuzzy authentication allows authentication based on the fuzzy matching of two
objects, for example based on the similarity of two strings in the Hamming
metric, or on the similiarity of two sets in the set difference metric. Aim of
this paper is to show other models and algorithms of secure fuzzy
authentication, which can be performed using the rank metric. A few schemes are
presented which can then be applied in different scenarios and applications.Comment: to appear in Cryptography and Physical Layer Security, Lecture Notes
in Electrical Engineering, Springe
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