Article ID Journal Published Year Pages File Type
6416679 Linear Algebra and its Applications 2013 10 Pages PDF
Abstract

In this article, we give upper bounds for cyclotomic numbers of order e over a finite field with q elements, where e is a positive divisor of q − 1. In particular, we show that under certain assumptions, cyclotomic numbers are at most ⌈k2⌉, and the cyclotomic number (0, 0) is at most ⌈k2⌉-1, where k=(q-1)/e. These results are obtained by using a known formula for the determinant of a matrix whose entries are binomial coefficients.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
, , , ,