Optimum Symbol-by-Symbol Signal Reception Using Linear Codes over GF(2~m)

摘要

An extension of the Walsh functions onto the Galois fields GF(2~m) is introduced. Fields with a simple relation between the traditional and extended Walsh functions are found. For a memoryless channel, an algorithm of the optimum symbol-by-symbol reception of signals based on linear codes over GF(2~m) is synthesized. The algorithm uses a fast spectral transform in the Walsh basis (FWT).