Digit systems in polynomial rings over finite fields
نویسندگان
چکیده
منابع مشابه
Factoring in Skew-Polynomial Rings over Finite Fields
Efficient algorithms are presented for factoring polynomials in the skew-polynomial ring F[x; σ], a non-commutative generalization of the usual ring of polynomials F[x], where F is a finite field and σ: F → F is an automorphism (iterated Frobenius map). Applications include fast functional decomposition algorithms for a class of polynomials in F[x] whose decompositions are “wild” and previously...
متن کاملClassical wavelet systems over finite fields
This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...
متن کاملCodes over finite quotients of polynomial rings
Codes over finite quotient of polynomial rings
متن کاملSolvability of Systems of Two Polynomial Equations over Finite Fields
In this paper we determine the solvability of families of systems of two polynomial equations over finite fields by computing the exact divisibility of the exponential sums associated to the systems. This generalizes a theorem of Carlitz to systems of two equations. Our result gives an upper bound for the Waring number of systems of diagonal equations. Also, as a by-product, we also obtain info...
متن کاملSolving systems of diagonal polynomial equations over finite fields
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the polynomial equations. Our algorithm works in time polynomial in the number of equations and the logarithm of the size of the field, whenever the degree of the pol...
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: 2003
ISSN: 1071-5797
DOI: 10.1016/s1071-5797(03)00008-x