On Fractional Decoding of Reed-Solomon Codes

Abstract

We define a virtual projection of a Reed-Solomon code RS(q l , n, k) to an RS(q, n, k) Reed-Solomon code. A new probabilistic decoding algorithm that can be used to perform fractional decoding beyond the αdecoding radius is considered. An upper bound for the failure probability of the new algorithm is given, and the performance is illustrated by examples.

Fractional decoding of r-Hermitian codes

“…To our knowledge, it is the first fractional decoding algorithm for codes from curves of positive genus. In [9] Santos provided a connection between fractional decoding of Reed-Solomon codes, which can be considered as codes from a curve of genus 0, the projective line, and collaborative decoding of interleaved Reed-Solomon codes. The codes considered in this paper are defined using the Hermitian curve y q + y = x q+1 over F q 2 , an integer r < q, and a constant field extension of the Riemann-Roch space of a divisor on this curve.…”

Fractional decoding and the Rosenbloom-Tsfasman metric

“…Santos [21] established a connection between fractional decoding of Reed-Solomon codes and collaborative decoding of interleaved Reed-Solomon codes [23]. In subsequent works [14] and [15], fractional decoding techniques were explored specifically for codes derived from Hermitian curves.…”