DocumentCode :
929849
Title :
Characterization theorems for extending Goppa codes to cyclic codes (Corresp.)
Author :
Tzeng, Kenneth K. ; Yu, Chie Y.
Volume :
25
Issue :
2
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 
and a Goppa polynomial 
that is irreducible over 
, then must be a quadratic. Goppa codes defined by 
and location set 
with cardinality 
such that 
are considered along with their subcodes. A sufficient condition on is derived for the extended codes to become cyclic. This condition is also necessary when 
= 1. The construction of for different 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.
and a Goppa polynomial that is irreducible over , then must be a quadratic. Goppa codes defined by and location set with cardinality such that are considered along with their subcodes. A sufficient condition on is derived for the extended codes to become cyclic. This condition is also necessary when = 1. The construction of for different 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 :
