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Calculations in Galois Fields
Calculations in Galois Fields By Ilya Pirkin, October 01, 2004 Galois fields are the basis for many forward error correction schemes used in computer communications. Ilya uses C++ templates and overloaded operations to implement them. Ilya Pirkin, who holds a masters degree in Physics from Moscow State University, works on real-time market information systems at CQG. He can be contacted at [email
Reed–Solomon codes for coders - Wikiversity
Error correcting codes are a signal processing technique to correct errors. They are nowadays ubiquitous, such as in communications (mobile phone, internet), data storage and archival (hard drives, optical discs CD/DVD/BluRay, archival tapes), warehouse management (barcodes) and advertisement (QR codes). Reed–Solomon error correction is a specific type of error correction code. It is one of the ol
よしいずの雑記帳 GF(2)上における多項式および既約多項式のリスト
5次以下の Z/2Z 係数多項式および Z/2Z 上既約な多項式のリスト。また、そのリストを使った整数係数多項式の既約性の判定。ただし、整数全体からなる集合を Z で表す。また、2個の元からなる有限体 Z/2Z は GF(2) とも書かれる。 5次以下の Z/2Z 係数多項式のリスト X [既約] 1+X [既約] X^2 1+X^2 = (1+X)^2 X+X^2 = (1+X)*X 1+X+X^2 [既約] X^3 1+X^3 = (1+X)*(1+X+X^2) X+X^3 = (1+X)^2*X 1+X+X^3 [既約] X^2+X^3 = (1+X)*X^2 1+X^2+X^3 [既約] X+X^2+X^3 = (1+X+X^2)*X 1+X+X^2+X^3 = (1+X)^3 X^4 1+X^4 = (1+X)^4 X+X^4 = (1+X)*(1+X+X^2)*X 1+X+X^
.:: Galois Field Arithmetic Library ::.
Description The branch in mathematics known as Galois theory (pronounced as "gal-wah") which is based on abstract algebra was discovered by a young brilliant french mathematician known as Evariste Galois. The branch deals mainly with the analysis and formal description of binary and unary operations upon polynomials comprised of elements within a Galois field that then describe polynomials within
Fast Galois Field Arithmetic Library in C/C++
James S. Plank plank@cs.utk.edu http://web.eecs.utk.edu/~jplank Technical Report UT-CS-07-593 Department of Computer Science University of Tennessee The online home for this document is: http://web.eecs.utk.edu/~jplank/plank/papers/CS-07-593 If You Use This Code Please send me email (plank@cs.utk.edu) and let me know. One of the ways in which I am evaluated is the impact of my work, and hard data
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Implementation of Galois field arithmetic
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Finite field arithmetic - Wikipedia