Create a Galois field

Create a Galois field

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);