Subcodes constructed from bases of Reed-Solomon codes

This paper proposes a method of constructing non-linear cyclic codes that form an additive group for which the decoding complexity or error correcting performance is improved relative to RS codes, which are typical linear cyclic codes. First, a code with information digit count k = 1 is constructed by using multiple RS code basis vectors obtained from Galois field Fourier transforms. Then, for k 1, codes are constructed from this code by using idempotent elements. Also, a code with code length n = 7 was constructed as an example, and both its minimal trellis diagram complexity and bit error rate on the AWGN channel due to a computer simulation were shown to be excellent. In addition, an iterative decoder was applied to the codes with k = 4 and 5, which had peak trellis diagram complexity, and it was shown that the decoding complexity could be reduced. (C) 2003 Wiley Periodicals, Inc.