Characterization theorems for extending Goppa codes to cyclic codes (Corresp.)

Author

Tzeng, Kenneth K. ; Yu, Chie Y.

Volume

Issue

fYear

1979

fDate

3/1/1979 12:00:00 AM

Firstpage

246

Lastpage

250

Abstract

Several theorems are presented which characterize Goppa codes having the property of becoming cyclic when an overall parity cheek is added. If such a Goppa code has location set $L = GF (q^{m})$ and a Goppa polynomial $g(z)$ that is irreducible over $GF(q^{m})$ , then $g(z)$ must be a quadratic. Goppa codes defined by $(z- \\beta )^{a}$ and location set $L$ with cardinality $n$ such that $n+l|q^{m}-1$ are considered along with their subcodes. A sufficient condition on $L$ is derived for the extended codes to become cyclic. This condition is also necessary when $a$ = 1. The construction of $L$ for different $n$ satisfying the stated condition is investigated in some detail. Some irreversible Goppa codes have been shown to become cyclic when extended by an overall parity check.

Keywords

Cyclic codes; Goppa codes; Helium; Parity check codes; Polynomials; Sufficient conditions;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1979.1056016

Filename

1056016

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=929849