Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Exponential sums and Goppa codes. I


Authors: Carlos J. Moreno and Oscar Moreno
Journal: Proc. Amer. Math. Soc. 111 (1991), 523-531
MSC: Primary 11T23; Secondary 11L40, 14G15, 94B40
MathSciNet review: 1028291
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A bound is obtained which generalizes the Carlitz-Uchiyama result, based on a theorem of Bombieri and Weil about exponential sums. This new bound is used to estimate the covering radius of long binary Goppa codes. A new lower bound is also derived on the minimum distance of the dual of a binary Goppa code, similar to that for BCH codes. This is an example of the use of a number-theory bound for the problem of the estimation of minimum distance of codes, as posed in research problem 9.9 of Mac Williams and Sloane, The Theory of Error Correcting Codes.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11T23, 11L40, 14G15, 94B40

Retrieve articles in all journals with MSC: 11T23, 11L40, 14G15, 94B40


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1028291-1
PII: S 0002-9939(1991)1028291-1
Article copyright: © Copyright 1991 American Mathematical Society