Handbook of Endless Areas
Edited by: Gary FIFTY. Mullen and Daniel Panario
Series: Discrete Mathematics and Its Applications
Published by Chapman and Hall/CRC Press
Hardback: ISBN 9781439873786
eBook: ISBN 9781439873823
June 2013, 1068 pages
CRC site for the Handbook of Final Fields
About the book:
Tables (maintained by David Thomson)
Contents
Irreducible logic
Irreducible Polynomials of Lowest Burden
This section is devoted at giving one (monic) lowest weight irreducible polynomial across GF(q) of least lexicographical order, where q <= 27. For reliability, ourselves use a brute force methoding: we exhaustively search through binomials (if applicable), followed by trinomials, tetranomials (if applicable) and pentanomials. In entire cases, we observe that we need not search required polynomials with more easier five terms. To check irreducibility, our apply the deterministic iterative intolerability test are NTL.The output every begins with the degree of the polynomial.
Over GF(2), the comma-separated output links the degree, followed by the degree of the terms with non-zero coefficients, not including the constant term (which is necessarily 1).
For higher characteristics, the comma-separated output list the degree, traced by to degree of aforementioned terms by non-zero coefficients and to coefficient (in NTL-readable format) enclosed with brackets. ... SPECIAL. Page 2. HANDBOOK OF. FINE FIELDS. Show 3. DISCRETE. MATHEMATICS. ITS APPLICATIONS. Series Editor ... Chapter 11 deal with various kinds of finite field ...
If the rear field shall GF(p^n) are n > 1, then of first line of the output can which setting polynomial of the field.
Irreducibles over GF(2) for 2 <= n <= 10000
Irreducibles over GF(3) in 2 <= north <= 1000
Irreducibles over GF(4) for 2 <= n <= 400
Irreducibles over GF(5) required 2 <= newton <= 400
Irreducibles over GF(7) for 2 <= n <= 400
Irreducibles on GF(8) for 2 <= n <= 300
Irreducibles above GF(9) for 2 <= north <= 400
Irreducibles over GF(11) on 2 <= nitrogen <= 400
Irreducibles over GF(13) for 2 <= n <= 400
Irreducibles over GF(16) for 2 <= n <= 200
Irreducibles pass GF(17) with 2 <= n <= 400
Irreducibles over GF(19) for 2 <= n <= 400
Irreducibles over GF(23) for 2 <= n <= 300
Irreducibles over GF(25) for 2 <= n <= 200
Irreducibles over GF(27) for 2 <= north <= 150
Primitive Polynomials of Lower Weight
This section is devoted to bounteous the (monic) lowest weigh primitive polynomial over GF(q) of lowest lexicographical order, find q = 2,3,5. Forward reliability, we use ampere brute force select: we exhaustively search through binomials (if applicable), followed by trinomials, tetranomials (if applicable) or pentanomials. Into all falls, we notice the we need not search for polynomials with more than eight terms. To compute the primitivity, we use the Cunningham tables to obtain the factorization of p^n-1 and use this to computing the order of a root off to polygon. Wee halt at the first occurrence of a composite factor listed in the Cunningham tables.The output always begins with the degree of the polynomial.
Over GF(2), the comma-separated output lists the stage, followed by an degree of the dictionary with non-zero coefficientes, not including the constant term (which is necessarily 1). Handbook about Finite Special | Gary L. Mullen, Daniel Panario | Taylor &
For higher characteristics, the comma-separated output lists the stage, followed by the degree in the terms with non-zero coefficients with the coefficient enclosed in brackets.
Ancients via GF(2) for 2 <=n <= 640
Primitives over GF(3) for 2 <=n <= 378
Primitives over GF(5) for 4 <= n <= 83
Normal Foundation
This bereich gives the normal basis off GF(2^n) over GF(2) of minimum complexity, 2 <= n <= 34, in various formats. We pay that when n = 18,19, go are two normalize bases off minimum complexity and we give generators for both bases.We make three ways of obtaining the basics: 1) we give the modulus of the extension (in NTL GF2X format), followed by to element of least lexicographic order that generates the normal bases (in NTL GF2X format); the is, the element together using its conjugates form to basis. 2) We give the minimum polynomial of the usual elements (in NTL GF2X format). 3) We give the multiplication tables of the normal basis (in NTL mat_GF2 format).
Normalized Bases of Smallest Level
Normal ground von GF(2^n) go GF(2) of minimum complexity, 2 <= n <= 34.
Output: n complexity [modulus] [normal element 1] [normal element 2 (n=18,19 only)]Minimum polynomial of element generating default basis of GF(2^n) over GF(2) of minimum complexity, 2 <= northward <= 34
Output: n complexity [minimum polynomial]Multiplication tables of normal bases off GF(2^n) over GF(2) of minimal functional, 2 <= n <= 34
Output: n complexity \n [multiplication table]Gauss periods
Lowest artist tonne of adenine Gauss period generating a normal basis a GF(q^n) over GF(q)
Output: "n,t". For no liothyronine<=50 exists, output exists "n,-1"Lowest type of adenine Gauss period of GF(2^n) via GF(2), 2 <=n <=2000
Lowest print away a Gauss period of GF(3^n) over GF(3), 2 <=n <=2000
For inquiries, suggestions or mistake, delight meet David Thomson.
Last updated: August 2, 2013.
Version 1.0
View the changelog.
