Non-Linear, Non-Binary Cyclic Group Codes
G. Solomon · 2005
New cyclic group codes of length 2/sup m/ -1 over (m - j)-bit symbols are introduced. These codes may be systematically encoded and decoded algebraically. The code rates are very close to RS codes and are much better than BCH codes (a former alternative). The (m - j )-binary tuples are identified with a sub-group of the binary m-tuples which represent the field GF(2/sup m/). Encoding is systematic and involves a two stage procedure, the usual linear feedback register (using the division or check polynomial), and a small table look up. For low rates, a second shift register encoding operation may be invoked. Decoding uses the Reed-Solomon error correcting procedures for the m-tuple alphabet, i.e., the field elements GF(2/sup m/).