( Fall 2007 ) Lecture 12 : Reed - Solomon Codes
نویسندگان
چکیده
We begin with the definition of Reed-Solomon codes. Definition 1.1 (Reed-Solomon code). Let Fq be a finite field and Fq[x] denote the Fq-space of univariate polynomials where all the coefficients of x are from Fq. Pick {α1, α2, ...αn} distinct elements (also called evaluation points) of Fq and choose n and k such that k ≤ n ≤ q. We define an encoding function for Reed-Solomon code as RS : Fq → F n q as follows. A message m = (m0, m1, ..., mk−1) with mi ∈ Fq is mapped to a degree k − 1 polynomial.
منابع مشابه
A general construction of Reed-Solomon codes based on generalized discrete Fourier transform
In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes enjoy nice algebraic properties just as the classic one.
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