IJPAM: Volume 19, No. 2 (2005)

IMPROVEMENT OF AX-KATZ'S AND
MORENO-MORENO'S RESULTS AND APPLICATIONS

Oscar Moreno$^1$, Francis N. Castro$^2$
$^1$Department of Computer Sciences
University of Puerto Rico
Rio Piedras, P.O. Box 23355 SJ, 00931-3355, PUERTO RICO
$^1$e-mail: moreno@uprr.pr
$^2$Department of Mathematics
University of Puerto Rico
Rio Piedras, P.O. Box 23355 SJ, 00931-3355, PUERTO RICO
$^2$e-mail: fcastro@goliath.cnnet.clu.edu


Abstract.In this paper we introduce the $p^m$-weight degree of a polynomial and using techniques of Ax-Katz, Moreno-Moreno and Adolphson-Sperber, we improve results of Ax-Katz, Moreno-Moreno and Adolphson-Sperber. Finally, we apply divisibility results to the Waring's problem and to the calculation of the covering radius of primitive codes with three zeros.

Received: February 8, 2005

AMS Subject Classification: 11T06, 11T23

Key Words and Phrases: Ax-Katz Theorem, Moreno-Moreno Theorem, Adolphson-Sperber Theorem, $p^m$-weight degree of a polynom

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 19
Issue: 2