Solving The Welch-Berlekamp Key Equation Over A Galois Ring

– The Welch-Berlekamp (WB) key equation arises in the decoding of Reed-Solomon (RS) codes over finite fields where the decoding problem is viewed as a rational interpolation problem. The significance of this decoding approach lies in the fact that it does not require the prior evaluation of power sum symmetric functions, i.e. the so-called syndrome vector corresponding to a received word. It has recently been shown that RS codes over Zq, q a prime power, can also be decoded in the same way as their field counterparts. The purpose of this paper is therefore to present a generalization of a WB-type algorithm for solving the key equation over a Galois ring. Key-Words: – Rational interpolation, Reed-Solomon codes, Welch-Berlekamp key equation, Galois rings.