In this paper a recursive form of Welch-Berlekamp (W-B) algorithm is provided which is a novel and fast decoding algorithm.

In this paper, we provide an efficient algorithm for GMD (Generalized Minimum Distance) decoding of BCH codes over q-valued logic, when q is pl (p: prime number, l: positive integer). An algebraic errors-and-erasures decoding procedure is required to execute only one time, whereas in a conventional GMD decoding at mostd/2algebraic decodings are necessary, where d is the design distance of the code. In our algorithm, Welch-Berlekamp's iterative method is efficiently employed to reduce the number of algebraic decoding procedures. We also show a method for hardware implementation of this GMD decoding based on q-valued logic.