Frequency-time codes based on the decimation method
A regular rule for building uniform frequency-time codes, having length p and a large volume, over the Galois prime fields GF(p) based on the decimation method has been proposed. It was shown that the noise immunity coefficient of the decimation code proposed was higher than the uniform Reed-Solomon codes built over the corresponding fields GF(p).
M. I. Mazurkov, “Augmented frequency–time codes of quadratic–cubic residues in Galois prime fields,” Radioelectron. Commun. Syst. 41(3), 50 (1998).
M. I. Mazurkov, “Frequency–time codes of quadratic residues in Galois augmented fields,” Radioelectron. Commun. Syst. 40(12), 22 (1997).
M. I. Mazurkov and V. S. Dmitrenko, “A Regular Rule for Generation of Full Classes of Optimal Systems of DF-Signals Based on the Method of Decimation,” Radioelectron. Commun. Syst. 48(2), 38 (2005).
M. I. Mazurkov, “Generalized Algorithms and Codec Diagrams of Algebraic Frequency–Time Codes of Power Residues”, Radioelectron. Commun. Syst. 42(3), 32 (1999).
M. I. Mazurkov and S. V. Mits, “The Method of Probabilistic Decoding of Reed–Solomon Cyclic Codes,” Radioelectron. Commun. Syst. 42(7), 11 (1999).
L. E. Varakin, Communications Systems with Noise-Like Signal (Radio i Svyaz’, Moscow, 1985) [in Russian].
I. M. Vinogradov, Basic Theory of Numbers (Nauka, Moscow, 1981) [in Russian].
R. Blahut, Theory and Practice of Error Control Codes (Addison-Wesley Publishing Company Inc., California–London–Amsterdam, 1983; Mir, Moscow, 1986).