boofcv.alg.fiducial.qrcode

Class GaliosFieldOps

java.lang.Object

boofcv.alg.fiducial.qrcode.GaliosFieldOps

public class GaliosFieldOps
extends java.lang.Object

Basic path operators on polynomial Galious Field (GF) with GF(2) coefficients. Polynomials are stored inside of integers with the least significant bits first. This class is primarily used to populate precomputed tables.

Code and code comments based on the tutorial at [1].

[1] Reed-Solomon Codes for Coders Viewed on September 28, 2017

Constructor Summary

Constructors

Constructor and Description
GaliosFieldOps()

Method Summary

Modifier and Type	Method and Description
static int	add(int a, int b)
static int	divide(int dividend, int divisor) Divides dividend by the divisor and returns the integer results, e.g.
static int	length(int value) The bit in which the most significant non-zero bit is stored
static int	modulus(int dividend, int divisor) Performs the polynomial GF modulus operation.
static int	multiply(int a, int b) Multiply the two polynomials together.
static int	multiply(int x, int y, int primitive, int domain) Implementation of multiplication with a primitive polynomial.
static int	subtract(int a, int b)

Methods inherited from class java.lang.Object

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

Constructor Detail

GaliosFieldOps

public GaliosFieldOps()

Method Detail

add

public static int add(int a,
                      int b)

subtract

public static int subtract(int a,
                           int b)

multiply

public static int multiply(int a,
                           int b)

Multiply the two polynomials together. The technique used here isn't the fastest but is easy to understand.

NOTE: No modulus operation is performed so the result might not be a member of the same field.

Parameters:

a - polynomial

b - polynomial

Returns:

result polynomial

multiply

public static int multiply(int x,
                           int y,
                           int primitive,
                           int domain)

Implementation of multiplication with a primitive polynomial. The result will be a member of the same field as the inputs, provided primitive is an appropriate irreducible polynomial for that field. Uses 'Russian Peasant Multiplication' that should be a faster algorithm.

Parameters:

x - polynomial

y - polynomial

primitive - Primitive polynomial which is irreducible.

domain - Value of a the largest possible value plus 1. E.g. GF(2**8) would be 256

Returns:

result polynomial

modulus

public static int modulus(int dividend,
                          int divisor)

Performs the polynomial GF modulus operation.

result = dividend mod divisor.

divide

public static int divide(int dividend,
                         int divisor)

Divides dividend by the divisor and returns the integer results, e.g. no remainder.

result = dividend / divisor

Parameters:

dividend - number on top

divisor - number on bottom

Returns:

number of times divisor goes into dividend.

length

public static int length(int value)

The bit in which the most significant non-zero bit is stored