A Proposed Algorithm for Generating the Reed-Solomon Encoding Polynomial Coefficients over GF(256) for RS[255,223]8,32

The ability to detect and correct data loss is of crucial importance to securing and recovering data stored on any storage facility (most importantly, the cloud). Reed-Solomon (RS) codeword is the most used for achieving this purpose. RS codeword is widely used for detecting and recovering data transmission errors as well as data loss in storage. This paper illustrates how the coefficients of the encoding polynomial needed for the generation of the RS codeword are generated. An efficient algorithm for generating the encoding polynomial coefficient is proposed. The algorithm is implemented in JAVA for Galois Field [GF(256)] with 32 parity shards – RS[255,223]8,32 to obtain an array of 32 coefficients as follows: {232, 29,189, 50, 142, 246, 232, 15, 43, 82, 164, 238, 1, 158, 13, 119, 158, 224, 134, 227, 210, 163, 50, 107, 40, 27, 104, 253, 24, 239, 216,45}