Cyclotomic orthomorphisms of finite fields
نویسندگان
چکیده
منابع مشابه
Cyclotomic R-orthomorphisms of finite fields
A polynomial f (X) over a finite field is an orthomorphism if both f (X) and f (X) − X are permutation polynomials. We prove the existence of several classes of cyclotomic orthomorphisms and extend the results toR-orthomorphisms. © 2005 Elsevier B.V. All rights reserved.
متن کاملAtomic Latin Squares based on Cyclotomic Orthomorphisms
Atomic latin squares have indivisible structure which mimics that of the cyclic groups of prime order. They are related to perfect 1-factorisations of complete bipartite graphs. Only one example of an atomic latin square of a composite order (namely 27) was previously known. We show that this one example can be generated by an established method of constructing latin squares using cyclotomic or...
متن کاملOn cyclotomic schemes over finite near-fields
We introduce a concept of cyclotomic association scheme over a finite near-field K. It is proved that any isomorphism of two such nontrivial schemes is induced by a suitable element of the group AGL(V ), where V is the linear space associated with K. A sufficient condition on a cyclotomic scheme C that guarantee the inclusion Aut(C)≤ A L(1,F), where F is a finite field with |K| elements, is given.
متن کاملExplicit factorizations of cyclotomic polynomials over finite fields
In this paper, we make an attempt to study the explicit factorization of 2.7-th cyclotomic polynomials over finite field Fq when q ≡ 1(mod 4) into a product of distinct monic irreducible polynomials, where q is a power of an odd prime. AMS Subject Classification: 11T06, 11T22, 12Y05
متن کاملOn the Reducibility of Cyclotomic Polynomials over Finite Fields
The irreducibility of a polynomial in a prime modulus implies irreducibility over the rationals. However, the converse is certainly not true. In fact, there are some polynomials that are irreducible over the rationals yet reducible in every prime modulus. We show that the nth cyclotomic polynomial reduces modulo all primes if and only if the discriminant of the nth cyclotomic polynomial is a sq...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.08.013