Patent ID: 6912240

Claim:
A method of generating a family of number sequences, comprising the steps of: specifying a prime number, p, having magnitude greater than 3 and an associated Galois field, GF(p); selecting a first primitive element of GF(p), α, and a second primitive element of GF(p), β, wherein α=β or a α≠β; defining a family of p+1 polynomials, wherein k is an integer and 0≦k≦p, wherein f k (x)=mod p (x 2 +x+k) when k<p and f k (x)=mod p (x+1) when k=p; defining a family of p+1 matrices, wherein each matrix, A (k) , has dimension (p−1)×(p−1) and the element of row i in column j of matrix A (k) , A (k) ij , is defined to have a first state when f k (α j )=mod p (β i ) and is otherwise defined to have a second state; and producing a family of p+1 number sequences, wherein the values of members of each number sequence, S k , are determined in accordance with the elements of a corresponding matrix, A (k) , of said family of p+1 matrices.