论文信息 - Polynomial codes

Polynomial codes

A class of cyclic codes is introduced by a polynomial approach that is an extension of the Mattson-Solomon method and of the Muller method. This class of codes contains several important classes of codes as subclasses, namely, BCH codes, Reed-Solomon codes, generalized primitive Reed-Muller codes, and finite geometry codes. Certain fundamental properties of this class of codes are derived. Some subclasses are shown to be majority-logic decodable.

[1] Jean-Marie Goethals,et al. On a class of majority-logic decodable cyclic codes , 1968, IEEE Trans. Inf. Theory.

[2] G. Solomon,et al. A New Treatment of Bose-Chaudhuri Codes , 1961 .

[3] David E. Muller,et al. Application of Boolean algebra to switching circuit design and to error detection , 1954, Trans. I R E Prof. Group Electron. Comput..

[4] Tadao Kasami,et al. New generalizations of the Reed-Muller codes-I: Primitive codes , 1968, IEEE Trans. Inf. Theory.

[5] E. J. Weldon,et al. New generalizations of the Reed-Muller codes-II: Nonprimitive codes , 1968, IEEE Trans. Inf. Theory.

[6] E. Weldon. Difference-set cyclic codes , 1966 .

[7] Dwijendra K. Ray-Chaudhuri,et al. Binary mixture flow with free energy lattice Boltzmann methods , 2022, arXiv.org.

[8] I. Reed,et al. Polynomial Codes Over Certain Finite Fields , 1960 .

[9] R. Graham,et al. On the number of information symbols in difference-set cyclic codes , 1966 .