Efficient Encoding for Generalized Reed Solomon Codes

Generalized Reed Solomon (GRS) codes are widely used for reliability applications in computer systems like data storage and communications and thus, efficiency in encoding and decoding of GRS codes is very important for system performance. Though GRS codes provide enormous flexibility, they are computationally expensive since calculations happen in Galois fields. In this paper, we present an algorithm to reduce the number of field multiplications in the encoding process of the GRS codes by selecting good values of $\bm{\alpha}$ and $\bm{w}$, the parameters of a GRS code. These values are usually set to some default value but by finding good values for these parameters using our algorithm we present here, we can impose a structure on the encoding matrix which enables significant reduction in the number of multiplications to enable efficient encoding. Our method provides from 25\% to over 90\% reduction in the number of multiplications depending on the code attributes.