Homogeneous Interpolation Problem and Key Equation for Decoding Reed-Solomon Codes
Dingjia Xin · Science in China Series A-Mathematics Physics Astronomy & Technological Science · 1994
The concept of homogeneous interpolation problem (HIP) over fields is introduced.It is discovered that solving HIP over finite fields is equivalent to decoding Reed-Solomon (RS) codes.The Welch-Berlekamp algorithm of decoding RS codes is derived;besides,by introducing the concept of incomplete locator of error patterns,the algorithm called incomplete iterative decoding is established.