Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416679 | Linear Algebra and its Applications | 2013 | 10 Pages |
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 â 1. In particular, we show that under certain assumptions, cyclotomic numbers are at most âk2â, and the cyclotomic number (0, 0) is at most âk2â-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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Koichi Betsumiya, Mitsugu Hirasaka, Takao Komatsu, Akihiro Munemasa,