R: Create a Galois field

create_galois_field {lhs} | R Documentation

## Create a Galois field

### Description

Create a Galois field

### Usage

    create_galois_field(q)

### Arguments

`q` | The order of the Galois Field q = p^n

### Value

a GaloisField object containing

n

  q = p^n

p

  The prime modulus of the field q=p^n

q

  The order of the Galois Field q = p^n. `q` must be a prime power.

xton

  coefficients of the characteristic polynomial where the first coefficient is on $x^0$, the second is on $x^1$ and so on

inv

  An index for which row of `poly` (zero based) is the multiplicative inverse of this row. An `NA` indicates that this row of `poly` has no inverse. e.g. c(3, 4) means that row 4=3+1 is the inverse of row 1 and row 5=4+1 is the inverse of row 2

neg

  An index for which row of `poly` (zero based) is the negative or additive inverse of this row. An `NA` indicates that this row of `poly` has no negative. e.g. c(3, 4) means that row 4=3+1 is the negative of row 1 and row 5=4+1 is the negative of row 2

root

  An index for which row of `poly` (zero based) is the square root of this row. An `NA` indicates that this row of `poly` has no square root. e.g. c(3, 4) means that row 4=3+1 is the square root of row 1 and row 5=4+1 is the square root of row 2

plus

  sum table of the Galois Field

times

  multiplication table of the Galois Field

poly

  rows are polynomials of the Galois Field where the entries are the coefficients of the polynomial where the first coefficient is on $x^0$, the second is on $x^1$ and so on

### Examples

    gf <- create_galois_field(4);

[Package lhs version 1.1.2 Index]