论文信息 - Quasicyclic irreducible Goppa codes

Quasicyclic irreducible Goppa codes

We establish the existence and give constructions of two new classes of quasicyclic irreducible Goppa codes. We give simple numerical conditions on the degree of the Goppa polynomial and length of an irreducible Goppa code which are sufficient conditions for it to be a member of one of these classes.

Patrick Fitzpatrick | John A. Ryan

[1] T. Berger. On the Cyclicity of Goppa Codes, Parity-Check Subcodes of Goppa Codes, and Extended Goppa Codes , 2000 .

[2] Patrick Fitzpatrick,et al. The number of inequivalent irreducible Goppa codes , 2001, Electron. Notes Discret. Math..

[3] J. A. Ryan,et al. Counting irreducible Goppa codes , 2001, Journal of the Australian Mathematical Society.

[4] Grégoire Bommier,et al. Binary Quasi-Cyclic Goppa Codes , 2000, Des. Codes Cryptogr..

[5] Patrick Fitzpatrick,et al. Algebraic structure of quasicyclic codes , 2001, Discret. Appl. Math..

[6] Chin-Long Chen. Equivalent irreducible Goppa codes (Corresp.) , 1978, IEEE Trans. Inf. Theory.

[7] Thierry P. Berger. Goppa and related codes invariant under a prescribed permutation , 2000, IEEE Trans. Inf. Theory.

[8] Harald Niederreiter,et al. Introduction to finite fields and their applications: List of Symbols , 1986 .