itpp::GF Class Reference

Galois Field GF(q). More...

#include <itpp/comm/galois.h>

Public Member Functions
	GF ()
	Constructor.
	GF (int qvalue)
	Constructor.
	GF (int qvalue, int inexp)
	Constructor.
	GF (const GF &ingf)
	Copy constructor.
void	set (int qvalue, int inexp)
	GF(q) equals alpha ^ inexp.
void	set (int qvalue, const bvec &vectorspace)
	GF(q) equals the element that corresponds to the given vector space.
void	set_size (int qvalue)
	set q=2^mvalue
int	get_size () const
	Return q.
bvec	get_vectorspace () const
	Returns the vector space representation of GF(q).
int	get_value () const
	Returns the alpha exponent.
int	operator== (const GF &ingf) const
	Equality check.
int	operator!= (const GF &ingf) const
	Not-equality check.
void	operator= (const GF &ingf)
	GF(q) equals ingf.
void	operator= (const int inexp)
	GF(q) equals alpha^inexp.
void	operator+= (const GF &ingf)
	sum of two GF(q)
GF	operator+ (const GF &ingf) const
	sum of two GF(q)
void	operator-= (const GF &ingf)
	Difference of two GF(q), same as sum for q=2^m.
GF	operator- (const GF &ingf) const
	Difference of two GF(q), same as sum for q=2^m.
void	operator*= (const GF &ingf)
	product of two GF(q)
GF	operator* (const GF &ingf) const
	product of two GF(q)
void	operator/= (const GF &ingf)
	division of two GF(q)
GF	operator/ (const GF &ingf) const
	product of two GF(q)

Friends
ITPP_EXPORT friend std::ostream &	operator<< (std::ostream &os, const GF &ingf)
	Output stream for GF(q)
ITPP_EXPORT friend std::istream &	operator>> (std::istream &is, GF &ingf)
	Input stream for GF(q)

Detailed Description

Galois Field GF(q).

Author

Tony Ottosson

Galois field GF(q), where q = 2^m. Possible m values is m = 1,2,...,16. Elements are given as exponents of the primitive element alpha. Observe that the zeroth element are given as "-1". ( log(0)=-Inf ).

The following primitve polynomials are used to construct the fields:

• GF(4): 1+x+x^2
• GF(8): 1+x+x^3
• GF(16): 1+x+x^4
• GF(32): 1+x^2+x^5
• GF(64): 1+x^2+x^6
• GF(128): 1+x^3+x^7
• GF(256): 1+x^2+x^3+x^4+x^8
• GF(512): 1+x^4+x^9
• GF(1024): 1+x^3+x^10
• GF(2^11): 1+x^2+x^11
• GF(2^12): 1+x+x^4+x^12
• GF(2^13): 1+x+x^3+x^4+x^13
• GF(2^14): 1+x+x^3+x^5+x^14
• GF(2^15): 1+x+x^15
• GF(2^16): 1+x+x^3+x^12+x^16

As indicated it is possible to use this class for binary elements, that is GF(2). However, this is less efficient in storage (each element take 5 bytes of memory) and in speed. If possible use the class BIN instead. Observe, also that the element "0" is called "-1" and "1" called "0".

Definition at line 74 of file galois.h.

Member Function Documentation

void itpp::GF::set ( int  qvalue, const bvec &  vectorspace  )

inline

GF(q) equals the element that corresponds to the given vector space.

The format is (...,c,b,a), where the element x is given as x=...+c*alpha^2+b*alpha+a.

Definition at line 269 of file galois.h.

References itpp::bin2dec(), it_assert_debug, and set_size().

bvec itpp::GF::get_vectorspace ( ) const

inline

Returns the vector space representation of GF(q).

The format is (...,c,b,a), where the element x is given as x=...+c*alpha^2+b*alpha+a.

Definition at line 276 of file galois.h.

References itpp::dec2bin().

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The documentation for this class was generated from the following files:

• itpp/comm/galois.h
• itpp/comm/galois.cpp