Algebraic Codes in the Frequency Domain
Communication theory and signal processing are closely related subjects that have been developed largely by engineers. Analysis and synthesis problems in these fields depend heavily on reasoning in the frequency domain. Thus, in the study of real- or complex-valued signals, the Fourier transform plays a basic role. When the time variable is discrete, the discrete Fourier transform plays a parallel role. Accordingly, Fourier transforms and discrete Fourier transforms are among the major tools of engineers.
KeywordsCyclic Code Parity Frequency Information Symbol Parity Check Matrix Error Control Code
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- 2.Gore, W.C., “Transmitting Binary Symbols With Reed-Solomon Codes,” Proceedings of Princeton Conference on Information Sciences and Systems, Princeton, N.J., pp 495–497, 1973.Google Scholar
- 3.Micheison, A., “A Fast Transform in Some Galois Fields and an Application to Decoding Reed-Solomon Codes,” IEEE Abstracts of Papers — IEEE International Symposium on Information Theory, Ronneby, Sweden, 1976.Google Scholar
- 10.Chien, R.T., “A New Proof of the BCH Bound,” IEEE Trans. Information Theory, Vol IT 18, p. 541, July, 1972.Google Scholar
- 13.Helgert, H.H., “Alternant Codes,” Information and Control, pp 369–381, 1974.Google Scholar
- 19.Wolf, J.K., “Adding Two Information Symbols to Certain Nonbinary BCH Codes and Some Applications,” Bell Syst. Tech. J., pp 2405–2424, 1969.Google Scholar