de.flexiprovider.common.math.codingtheory
Class GoppaCode

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

public final class GoppaCode

extends java.lang.Object

This class describes decoding operations of an irreducible binary Goppa code. A check matrix H of the Goppa code and an irreducible Goppa polynomial are used the operations are worked over a finite field GF(2^m)

Author:

Elena Klintsevich, Martin Döring

See Also:

GF2mField, PolynomialGF2mSmallM

Inner Class Summary

static class	GoppaCode.MaMaPe This class is a container for two instances of GF2Matrix and one instance of Permutation.
static class	GoppaCode.MatrixSet This class is a container for an instance of GF2Matrix and one int[].

Method Summary

static GoppaCode.MaMaPe	computeSystematicForm(GF2Matrix h, SecureRandom sr) Given a check matrix H, compute matrices S, M, and a random permutation P such that S*H*P = (Id|M).
static GF2Matrix	createCanonicalCheckMatrix(GF2mField field, PolynomialGF2mSmallM gp) Construct the check matrix of a Goppa code in canonical form from the irreducible Goppa polynomial over the finite field GF(2m).
static GF2Vector	syndromeDecode(GF2Vector syndVec, GF2mField field, PolynomialGF2mSmallM gp, PolynomialGF2mSmallM[] sqRootMatrix) Find an error vector e over GF(2) from an input syndrome s over GF(2m).

Methods inherited from class java.lang.Object

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

Method Detail

createCanonicalCheckMatrix

public static GF2Matrix createCanonicalCheckMatrix(GF2mField field,
                                                   PolynomialGF2mSmallM gp)

Construct the check matrix of a Goppa code in canonical form from the irreducible Goppa polynomial over the finite field GF(2^m).

Parameters:

field - the finite field

gp - the irreducible Goppa polynomial

computeSystematicForm

public static GoppaCode.MaMaPe computeSystematicForm(GF2Matrix h,
                                                     SecureRandom sr)

Given a check matrix H, compute matrices S, M, and a random permutation P such that S*H*P = (Id|M). Return S^-1, M, and P as GoppaCode.MaMaPe. The matrix (Id | M) is called the systematic form of H.

Parameters:

h - the check matrix

sr - a source of randomness

Returns:

the tuple (S^-1, M, P)

syndromeDecode

public static GF2Vector syndromeDecode(GF2Vector syndVec,
                                       GF2mField field,
                                       PolynomialGF2mSmallM gp,
                                       PolynomialGF2mSmallM[] sqRootMatrix)

Find an error vector e over GF(2) from an input syndrome s over GF(2^m).

Parameters:

syndVec - the syndrome

field - the finite field

gp - the irreducible Goppa polynomial

sqRootMatrix - the matrix for computing square roots in (GF(2^m))^t

Returns:

the error vector