# Class GaliosFieldOps

java.lang.Object
boofcv.alg.fiducial.qrcode.GaliosFieldOps

public class GaliosFieldOps extends 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
Description
`GaliosFieldOps()`

• ## Method Summary

Modifier and Type
Method
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 Details

• ### GaliosFieldOps

public GaliosFieldOps()
• ## Method Details

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