• Corpus ID: 123858546

# 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}
}
• Published 2005
• Computer Science
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.
3 Citations
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
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
• Computer Science
• 2017
The covering radius of some families of binary cyclic codes with two zeros and minimum distance greater than 3.5m is computed.

## References

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A new method to obtain the covering radius of codes and a method to prove quasi-perfection in codes are presented, which answers a problem posed by Cohen-Honkala-Litsyn-Lobstein in the book covering radius for BCH codes.
• Mathematics, Computer Science
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A tight bound on the p‐divisibility of the exponential sums is derived which in several classes of examples, improve on the results of Chevalley and Warning, Ax and Katz, Adolphson and Sperber, and Moreno and Moreno.
• Computer Science
IEEE Trans. Inf. Theory
• 1986
A new lower bound for the minimum distance of cyclic codes that includes earlier bounds (i.e., BCH bound, HT bound, Roos bound) is created and can be even stronger than the first one.