de.flexiprovider.common.math.codingtheory
Class PolynomialRingGF2

java.lang.Object
  |
  +--de.flexiprovider.common.math.codingtheory.PolynomialRingGF2

public final class PolynomialRingGF2

extends java.lang.Object

This class describes operations with polynomials over finite field GF(2), i e polynomial ring R = GF(2)[X]. All operations are defined only for polynomials with degree <=32. For the polynomial representation the map f: R->Z, poly(X)->poly(2) is used, where integers have the binary representation. For example: X^7+X^3+X+1 -> (00...0010001011)=139 Also for polynomials type Integer is used.

Author:

Elena Klintsevich

See Also:

GF2mField

Method Summary

static int	add(int p, int q) Return sum of two polyomials
static int	degree(int p) Return the degree of a polynomial
static int	degree(long p) Return the degree of a polynomial
static int	gcd(int p, int q) Return the greatest common divisor of two polynomials
static int	getIrreduciblePolynomial(int deg) Creates irreducible polynomial with degree d
static boolean	isIrreducible(int p) Checking polynomial for irreducibility
static int	modMultiply(int a, int b, int r) Compute the product of two polynomials modulo a third polynomial.
static long	multiply(int p, int q) Return product of two polynomials
static int	remainder(int p, int q) Return the remainder of a polynomial division of two polynomials.
static int	rest(long p, int q) Return the rest of devision two polynomials

Methods inherited from class java.lang.Object

, clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

add

public static int add(int p,
                      int q)

Return sum of two polyomials

Parameters:

p - polynomial

q - polynomial

Returns:

p+q

multiply

public static long multiply(int p,
                            int q)

Return product of two polynomials

Parameters:

p - polynomial

q - polynomial

Returns:

p*q

modMultiply

public static int modMultiply(int a,
                              int b,
                              int r)

Compute the product of two polynomials modulo a third polynomial.

Parameters:

a - the first polynomial

b - the second polynomial

r - the reduction polynomial

Returns:

a * b mod r

degree

public static int degree(int p)

Return the degree of a polynomial

Parameters:

p - polynomial p

Returns:

degree(p)

degree

public static int degree(long p)

Return the degree of a polynomial

Parameters:

p - polynomial p

Returns:

degree(p)

remainder

public static int remainder(int p,
                            int q)

Return the remainder of a polynomial division of two polynomials.

Parameters:

p - dividend

q - divisor

Returns:

p mod q

rest

public static int rest(long p,
                       int q)

Return the rest of devision two polynomials

Parameters:

p - polinomial

q - polinomial

Returns:

p mod q

gcd

public static int gcd(int p,
                      int q)

Return the greatest common divisor of two polynomials

Parameters:

p - polinomial

q - polinomial

Returns:

GCD(p,q)

isIrreducible

public static boolean isIrreducible(int p)

Checking polynomial for irreducibility

Parameters:

p - polinomial

Returns:

true if p is irreducible and false otherwise

getIrreduciblePolynomial

public static int getIrreduciblePolynomial(int deg)

Creates irreducible polynomial with degree d

Parameters:

deg - polynomial degree

Returns:

irreducible polynomial p