9 research outputs found
Decoding of Interleaved Reed-Solomon Codes Using Improved Power Decoding
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 at all code rates , in time polynomial in the
code length . For , this is an asymptotic improvement over the previous
state-of-the-art for all rates, and the first improvement for in the
last years. The method combines collaborative decoding of IRS codes with
power decoding up to the Johnson radius.Comment: 5 pages, accepted at IEEE International Symposium on Information
Theory 201
Improved Power Decoding of One-Point Hermitian Codes
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 it has a similar failure probability as the
latter one. The algorithm is based on a recent generalization of the power
decoding algorithm for Reed--Solomon codes and does not require an expensive
root-finding step. In addition, it promises improvements for decoding
interleaved Hermitian codes.Comment: 9 pages, submitted to the International Workshop on Coding and
Cryptography (WCC) 201
Further Generalisations of Twisted Gabidulin Codes
We present a new family of maximum rank distance (MRD) codes. The new class
contains codes that are neither equivalent to a generalised Gabidulin nor to a
twisted Gabidulin code, the only two known general constructions of linear MRD
codes.Comment: 10 pages, accepted at the International Workshop on Coding and
Cryptography (WCC) 201
Twisted Reed-Solomon Codes
We present a new general construction of MDS codes over a finite field
. We describe two explicit subclasses which contain new MDS codes
of length at least for all values of . Moreover, we show that
most of the new codes are not equivalent to a Reed-Solomon code.Comment: 5 pages, accepted at IEEE International Symposium on Information
Theory 201