SYMMETRIES OF BINARY GOPPA CODES

被引：17

作者：

MORENO, O

机构：

[1] Department of Mathematics, University of Puerto Rico, Rio Piedras

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 1979年 / 25卷 / 05期

关键词：

D O I：

10.1109/TIT.1979.1056089

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

It is known that extended Goppa codes are invariant under the group of transformations Z -(AZ + B) / (CZ + D), with AD + BC =1= 0. This invariance is used here to classify cubic and quartic irreducible Goppa codes and to investigate their symmetry groups. A computer has been used to determine the actual group of the codes of length 33 (for cubics and quartics). It has been said, concerning the trends in symmetry groups with respect to the Gilbert bound, that “a good family of codes can be linear or have many symmetries, but not both” [8]. The groups found here are rather small; and so the results reinforce that statement. © 1979 IEEE

引用

页码：609 / 612

页数：4

共 9 条

[1] ON SOLUTION OF ALGEBRAIC EQUATIONS OVER FINITE FIELDS [J].

BERLEKAM.ER ;

RUMSEY, H ;

SOLOMON, G .

INFORMATION AND CONTROL, 1967, 10 (06) :553-&

[2] EXTENDED DOUBLE-ERROR-CORRECTING BINARY GOPPA CODES ARE CYCLIC [J].

BERLEKAMP, ER ;

MORENO, O .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1973, 19 (06) :817-818

[3] GOPPA CODES [J].

BERLEKAMP, ER .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1973, 19 (05) :590-592

[4]

BERLEKAMP ER, 1968, ALGEBRAIC CODING THE

[5]

Goppa V., 1970, PROBL PEREDA INF, V6, P24

[6]

Goppa V., 1971, PROBL PREDACH INFORM, V7, P41

[7]

HARTSHORNE R, 1967, F PROJECTIVE GEOMETR

[8]

MORENO O, 1973, THESIS U CALIF

[9]

Sloane N. J. A., 1972, Discrete Mathematics, V3, P265, DOI 10.1016/0012-365X(72)90036-2

← 1 →