Decoding of reed-solomon codes beyond the bch bound using euclidean algorithm

1996 ◽  
Vol 79 (3) ◽  
pp. 94-110
Author(s):  
Toshio Horiguchi
Keyword(s):  
Euclidean Algorithm ◽  
Reed Solomon Codes ◽  
Bch Bound

scholarly journals The Symmetric Key Equation for Reed–Solomon Codes and a New Perspective on the Berlekamp–Massey Algorithm

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1357
Author(s):  
Maria Bras-Amorós ◽  
Michael E. O’Sullivan
Keyword(s):  
Euclidean Algorithm ◽  
Reed Solomon Codes ◽  
Degree Bounds ◽  
Key Equation ◽  
Symmetric Key ◽  
New Perspective

This paper presents a new way to view the key equation for decoding Reed–Solomon codes that unites the two algorithms used in solving it—the Berlekamp–Massey algorithm and the Euclidean algorithm. A new key equation for Reed–Solomon codes is derived for simultaneous errors and erasures decoding using the symmetry between polynomials and their reciprocals as well as the symmetries between dual and primal codes. The new key equation is simpler since it involves only degree bounds rather than modular computations. We show how to solve it using the Euclidean algorithm. We then show that by reorganizing the Euclidean algorithm applied to the new key equation we obtain the Berlekamp–Massey algorithm.

Sign in / Sign up

Export Citation Format

Share Document