Exponential sums and Goppa codes. II

Author

Moreno, Carlos J. ; Moreno, Oscar

Author_Institution

Baruch Coll. & Graduate Center, City Univ. of New York, Salem, NY, USA

Volume

38

Issue

4

fYear

1992

fDate

7/1/1992 12:00:00 AM

Firstpage

1222

Lastpage

1229

Abstract

For pt.I, see Proc. AMS, vol.III, p.523-31 (1991). The minimum distance of a Goppa code is found when the length of code satisfies a certain inequality on the degree of the Goppa polynomial. In order to do this, conditions are improved on a theorem of E. Bombieri (1966). This improvement is used also to generalize a previous result on the minimum distance of the dual of a Goppa code. This approach is generalized and results are obtained about the parameters of a class of subfield subcodes of geometric Goppa codes; in other words, the covering radii are estimated, and further, the number of information symbols whenever the minimum distance is small in relation to the length of the code is found. Finally, a bound on the minimum distance of the dual code is discussed

Keywords

error correction codes; Goppa codes; Goppa polynomial; binary codes; covering radius; dual code; exponential sums; geometric codes; minimum distance; number of information symbols; subfield subcodes; Binary codes; Galois fields; Mathematics; Parameter estimation; Parity check codes; Sufficient conditions;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.144703

Filename

144703