Permutation polynomials and applications to coding theory
نویسندگان
چکیده
منابع مشابه
Permutation Groups and Polynomials
Given a set S with n elements, consider all the possible one-to-one and onto functions from S to itself. This collection of functions is called the permutation group of S, because the functions are simply permuting the elements of S. We notice immediately that it doesn’t matter what the elements of S are (numbers, planets, tacos, etc) just that there are n distinct ones in the set, so we may re...
متن کاملA general representation theory for constructing groups of permutation polynomials
Using the left regular action of a group on itself, we develop a general representation theory for constructing groups of permutation polynomials. As an application of the method, we compute polynomial representations of several abelian and nonabelian groups, and we determine the equivalence classes of the groups of polynomials we construct. In particular, when the size of the group is equal to...
متن کاملZeros of Polynomials and their Applications to Theory: A Primer
Problems in many different areas of mathematics reduce to questions about the zeros of complex univariate and multivariate polynomials. Recently, several significant and seemingly unrelated results relevant to theoretical computer science have benefited from taking this route: they rely on showing, at some level, that a certain univariate or multivariate polynomial has no zeros in a region. Thi...
متن کاملMultivariate Stable Polynomials: Theory and Applications
Univariate polynomials with only real roots, while special, do occur often enough that their properties can lead to interesting conclusions in diverse areas. Due mainly to the recent work of two young mathematicians, Julius Borcea and Petter Brändén, a very successful multivariate generalization of this method has been developed. The first part of this paper surveys some of the main results of ...
متن کاملSymplectic Spreads and Permutation Polynomials
Every symplectic spread of PG(3, q), or equivalently every ovoid of Q(4, q), is shown to give a certain family of permutation polynomials of GF (q) and conversely. This leads to an algebraic proof of the existence of the Tits-Lüneburg spread of W (2) and the Ree-Tits spread of W (3), as well as to a new family of low-degree permutation polynomials over GF (3). Let PG(3, q) denote the projective...
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: Finite Fields and Their Applications
سال: 2007
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2005.08.003