Speedier decoding of cyclic codes using chord properties

Finite-field transform quantities, appearing in typical cyclic code decoders, obey conjugacy-based relationships commonly called chord properties. It is demonstrated that these relationships may be used to significantly expedite error estimation by the decoder. The resulting speed-up factor is proportional to the degree of the extension field in which the code design is specified. BCH codes and standard decoder structures, either of the frequency-domain or time-domain type, are used to motivate, develop, and illustrate the underlying principles. Approximate estimates of the complexities and benefits of the proposed techniques are given. Finally, these chord-directed speed-up methods are extended to Reed-Solomon and other cyclic codes that use symbols in an extension field