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We provide a new approach to the elliptic curve discrete logarithm problem (ECDLP). First, we construct Elliptic Codes (EC codes) from the ECDLP. Then we propose an algorithm of finding the minimum we...
We describe a successive-cancellation \emph{list} decoder for polar codes, which is a generalization of the classic successive-cancellation decoder of Ar{\i}kan. In the proposed list decoder, up to $L...
An open question about Gabidulin codes is whether polynomial-time list decoding beyond half the minimum distance is possible or not. In this contribution, we give a lower and an upper bound on the lis...
Combinatorial limitations of a strong form of list decoding
Combinatorial limitations strong form of list decoding combinatorics
2012/2/29
We prove the following results concerning the combinatorics of list decoding, motivated by the exponential gap between the known upper bound (of $O(1/\gamma)$) and lower bound (of $\Omega_p(\log (1/\g...
An algorithm for list decoding number field codes
algorithm number field codes Number Theory
2011/9/5
Abstract: We present an algorithm for list decoding codewords of algebraic number field codes in polynomial time. This is the first explicit procedure for decoding number field codes whose constructio...
List-decoding of binary Goppa codes up to the binary Johnson bound
Error correcting codes, algebraic geometric codes list-decoding
2011/2/21
We study the list-decoding problem of alternant codes, with the notable case of classical Goppa codes. The major consideration here is to take into account the size of the alphabet, which shows great ...
A parametric approach to list decoding of Reed-Solomon codes using interpolation
list decoding of Reed-Solomon codes interpolation
2010/11/11
In this paper we present a minimal list decoding algorithm for Reed-Solomon (RS) codes. Minimal list decoding for a code $C$ refers to list decoding with radius $L$, where $L$ is the minimum of the d...