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

@inproceedings{Moreno2005IMPROVEMENTOA, title={IMPROVEMENT OF AX-KATZ'S AND MORENO-MORENO'S RESULTS AND APPLICATIONS}, author={Oscar Moreno and Francis N. Castro and R{\'i}o Piedras}, year={2005} }

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.

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## 3 Citations

### Chevalley Warning Theorems on abelian groups

- Mathematics
- 2019

A theorem of Chevalley states that a system of polynomial equations over a finite field cannot have exactly one solution if the number of variables is strictly greater than the sum of their total…

### Point count divisibility for algebraic sets over ${\mathbb {Z}}/p^\ell {\mathbb {Z}}$ and other finite principal rings

- Mathematics
- 2009

We determine the greatest common divisor of the cardinalities of the algebraic sets generated by collections of polynomials f 1 ,..., f t of specified degrees d 1, ...., dt in n variables over a…

### On the covering radius of some binary cyclic codes

- Computer ScienceAdv. Math. Commun.
- 2017

The covering radius of some families of binary cyclic codes with two zeros and minimum distance greater than 3.5m is computed.

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