gf

Documentation

Overview

Package gf implements arithmetic over Galois Fields. Generalized for any valid order.

Index

• type Field
  • func NewField(order, poly, α int) *Field
  • func (f *Field) Add(x, y byte) byte
  • func (f *Field) Exp(e int) byte
  • func (f *Field) Inv(x byte) byte
  • func (f *Field) Log(x byte) int
  • func (f *Field) Mul(x, y byte) byte
  • func (f *Field) Syndrome(message []byte, paritySymbolCount, offset int) (syndrome []byte)

Types

type Field

type Field struct {
	// contains filtered or unexported fields
}

A Field represents an instance of GF(order) defined by a specific polynomial.

func NewField

func NewField(order, poly, α int) *Field

NewField returns a new field corresponding to the polynomial poly and generator α. The choice of generator α only affects the Exp and Log operations.

func (*Field) Add

func (f *Field) Add(x, y byte) byte

Add returns the sum of x and y in the field.

func (*Field) Exp

func (f *Field) Exp(e int) byte

Exp returns the base-α exponential of e in the field. If e < 0, Exp returns 0.

func (*Field) Inv

func (f *Field) Inv(x byte) byte

Inv returns the multiplicative inverse of x in the field. If x == 0, Inv returns 0.

func (*Field) Log

func (f *Field) Log(x byte) int

Log returns the base-α logarithm of x in the field. If x == 0, Log returns -1.

func (*Field) Mul

func (f *Field) Mul(x, y byte) byte

Mul returns the product of x and y in the field.

func (*Field) Syndrome

func (f *Field) Syndrome(message []byte, paritySymbolCount, offset int) (syndrome []byte)

Calculate syndrome for a message encoded using the field generated for a particular Reed-Solomon polynomial. Offset defines the coefficient offset.