GenericGF (Javadocs [I2P+ 2.13.0+] - API Version 0.9.70+)

java.lang.Object
- com.google.zxing.common.reedsolomon.GenericGF

```
public final class GenericGF
extends Object
```
This class contains utility methods for performing mathematical operations over the Galois Fields. Operations use a given primitive polynomial in calculations.
Throughout this package, elements of the GF are represented as an int for convenience and speed (but at the cost of memory).

Field Summary

Fields
Modifier and Type	Field and Description
`static GenericGF`	`AZTEC_DATA_10` Galois field for Aztec 10-bit data symbols (1024 elements).
`static GenericGF`	`AZTEC_DATA_12` Galois field for Aztec 12-bit data symbols (4096 elements).
`static GenericGF`	`AZTEC_DATA_6` Galois field for Aztec 6-bit data symbols (64 elements).
`static GenericGF`	`AZTEC_DATA_8` Alias for DATA_MATRIX_FIELD_256.
`static GenericGF`	`AZTEC_PARAM` Galois field for Aztec parameter symbols (16 elements).
`static GenericGF`	`DATA_MATRIX_FIELD_256` Galois field for Data Matrix symbols (256 elements).
`static GenericGF`	`MAXICODE_FIELD_64` Alias for AZTEC_DATA_6.
`static GenericGF`	`QR_CODE_FIELD_256` Galois field for QR Code symbols (256 elements).

Constructor Summary
Constructors
Constructor and Description
GenericGF(int primitive, int size, int b)
Create a representation of GF(size) using the given primitive polynomial.

Constructors
Constructor and Description
`GenericGF(int primitive, int size, int b)` Create a representation of GF(size) using the given primitive polynomial.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`(package private) static int`	`addOrSubtract(int a, int b)` Implements both addition and subtraction -- they are the same in GF(size).
`(package private) GenericGFPoly`	`buildMonomial(int degree, int coefficient)`
`(package private) int`	`exp(int a)`
`int`	`getGeneratorBase()`
`(package private) GenericGFPoly`	`getOne()` Multiplicative identity (one polynomial).
`int`	`getSize()`
`(package private) GenericGFPoly`	`getZero()` Additive identity (zero polynomial).
`(package private) int`	`inverse(int a)`
`(package private) int`	`log(int a)`
`(package private) int`	`multiply(int a, int b)`
`String`	`toString()` Human-readable string representation of this Galois field.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Field Detail
  - AZTEC_DATA_10
```
public static final GenericGF AZTEC_DATA_10
```
    Galois field for Aztec 10-bit data symbols (1024 elements).
  - AZTEC_DATA_12
```
public static final GenericGF AZTEC_DATA_12
```
    Galois field for Aztec 12-bit data symbols (4096 elements).
  - AZTEC_DATA_6
```
public static final GenericGF AZTEC_DATA_6
```
    Galois field for Aztec 6-bit data symbols (64 elements).
  - AZTEC_DATA_8
```
public static final GenericGF AZTEC_DATA_8
```
    Alias for DATA_MATRIX_FIELD_256.
  - AZTEC_PARAM
```
public static final GenericGF AZTEC_PARAM
```
    Galois field for Aztec parameter symbols (16 elements).
  - DATA_MATRIX_FIELD_256
```
public static final GenericGF DATA_MATRIX_FIELD_256
```
    Galois field for Data Matrix symbols (256 elements).
  - MAXICODE_FIELD_64
```
public static final GenericGF MAXICODE_FIELD_64
```
    Alias for AZTEC_DATA_6.
  - QR_CODE_FIELD_256
```
public static final GenericGF QR_CODE_FIELD_256
```
    Galois field for QR Code symbols (256 elements).
- Constructor Detail
  - GenericGF
```
public GenericGF(int primitive,
                 int size,
                 int b)
```
    Create a representation of GF(size) using the given primitive polynomial.
    Parameters:
    primitive - irreducible polynomial whose coefficients are represented by the bits of an int, where the least-significant bit represents the constant coefficient
    size - the size
    b - the factor b in the generator polynomial can be 0- or 1-based (g(x) = (x+a^b)(x+a^(b+1))...(x+a^(b+2t-1))). In most cases it should be 1, but for QR code it is 0.
- Method Detail
  - addOrSubtract
```
static int addOrSubtract(int a,
                         int b)
```
    Implements both addition and subtraction -- they are the same in GF(size).
    Returns:
    sum/difference of a and b
  - buildMonomial
```
GenericGFPoly buildMonomial(int degree,
                            int coefficient)
```
    Returns:
    the monomial representing coefficient * x^degree
  - exp
```
int exp(int a)
```
    Returns:
    2 to the power of a in GF(size)
  - getGeneratorBase
```
public int getGeneratorBase()
```
    Returns:
    the generator base
  - getOne
```
GenericGFPoly getOne()
```
    Multiplicative identity (one polynomial).
  - getSize
```
public int getSize()
```
    Returns:
    the size
  - getZero
```
GenericGFPoly getZero()
```
    Additive identity (zero polynomial).
  - inverse
```
int inverse(int a)
```
    Returns:
    multiplicative inverse of a
  - log
```
int log(int a)
```
    Returns:
    base 2 log of a in GF(size)
  - multiply
```
int multiply(int a,
             int b)
```
    Returns:
    product of a and b in GF(size)
  - toString
```
public String toString()
```
    Human-readable string representation of this Galois field.
    Overrides:
    toString in class Object

Class GenericGF

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

AZTEC_DATA_10

AZTEC_DATA_12

AZTEC_DATA_6

AZTEC_DATA_8

AZTEC_PARAM

DATA_MATRIX_FIELD_256

MAXICODE_FIELD_64

QR_CODE_FIELD_256

Constructor Detail

GenericGF

Method Detail

addOrSubtract

buildMonomial

exp

getGeneratorBase

getOne

getSize

getZero

inverse

log

multiply

toString