论文信息 - Irreducible Cyclic Codes and Gauss Sums

Irreducible Cyclic Codes and Gauss Sums

In this paper we wish to point out the existence of a close connection between irreducible cyclic codes and Gauss sums over finite fields, and then to apply the well-developed theory of Gauss sums to the much less well-developed theory of irreducible cyclic codes.

R. McEliece

[1] L. Stickelberger,et al. Ueber eine Verallgemeinerung der Kreistheilung , 1890 .

[2] H. Hasse,et al. Die Nullstellen der Kongruenzzetafunktionen in gewissen zyklischen Fällen. , 1935 .

[3] Hermann Weyl,et al. Algebraic Theory of Numbers , 1940 .

[4] H. Hasse. Vorlesungen über Zahlentheorie , 1950 .

[5] I. Vinogradov,et al. Elements of number theory , 1954 .

[6] On Kummer Sums , 1970 .

[7] S. Lang. Algebraic Number Theory , 1971 .

[8] Jacobus H. van Lint,et al. Coding Theory , 1971 .

[9] R. McEliece,et al. Euler products, cyclotomy, and coding☆ , 1972 .

[10] Robert J. McEliece,et al. Weights of Irreducible Cyclic Codes , 1972, Inf. Control..

[11] L. D. Baumert,et al. Weight Distributions of Some Irreducible Cyclic Codes , 1973 .