Codes from incidence matrices and line graphs of Paley graphs

We examine the p-ary codes from incidence matrices of Paley graphs P (q) where q ≡ 1 (mod 4) is a prime power, and show that the codes are [ q(q−1) 4 , q − 1, q−1 2 ]2 or [ q(q−1) 4 , q, q−1 2 ]p for p odd. By finding PD-sets we show that for q > 9 the p-ary codes, for any p, can be used for permutation decoding for full error-correction. The binary code from the line graph of P (q) is shown to be the same as the binary code from an incidence matrix for P (q).