A Reed-Solomon code based on a new matrix transform.

摘要

Dr. Blahut has shown that Reed-Solomon codes can be formulated in terms of Fourier matrix transforms in Galois fields. Similarly, a new matrix transform that I call the polynomial coefficient transform can be used to formulate what I call PCT-codes. These PCT-codes have the same codeword length and error correction capabilities as a full length RS-code augmented with parity (p+RS-code), however PCT-codes have two advantages. The first advantage is that implementations of PCT-codes will tend to make somewhat fewer decoding errors than p+RS-codes. (A decoding error results when more errors occur in a received codeword than can be corrected, but the received codeword is corrected anyway.) The second advantage is that a simple auto-regressive filter can produce PCT-code codewords, that contain the information symbols as part of the codeword, in an integer Galois field.