Decoding Interleaved Gabidulin Codes using Alekhnovich's Algorithm
نویسندگان
چکیده
منابع مشابه
Decoding Interleaved Gabidulin Codes using Alekhnovich's Algorithm
We prove that Alekhnovich’s algorithm can be used for row reduction of skew polynomial matrices. This yields an O(ln log(n)) decoding algorithm for l-Interleaved Gabidulin codes of length n, where ω is the matrix multiplication exponent, improving in the exponent of n compared to previous results.
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In this paper we view interleaved Gabidulin codes and describe how to correct errors up to a rank equal to the amount of redundancy of the code with high probability. We give a detailed proof for our estimation of the probability of correct decoding. In a second part, we view the application to variants of the GPT cryptosystem. For GGPT this leads to an efficient attack on the remaining secure ...
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A new interpolation-based decoding principle for interleaved Gabidulin codes is presented. The approach consists of two steps: First, a multi-variate linearized polynomial is constructed which interpolates the coefficients of the received word and second, the roots of this polynomial have to be found. Due to the specific structure of the interpolation polynomial, both steps (interpolation and r...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2017
ISSN: 1571-0653
DOI: 10.1016/j.endm.2017.02.029