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).
CODES FROM INCIDENCE MATRICES AND LINE GRAPHS OF PALEY GRAPHS / Ghinelli, Dina; Key, J. D.. - In: ADVANCES IN MATHEMATICS OF COMMUNICATIONS. - ISSN 1930-5346. - STAMPA. - 5:(2011), pp. 98-108. [10.3934/amc.2011.5.93]
CODES FROM INCIDENCE MATRICES AND LINE GRAPHS OF PALEY GRAPHS
GHINELLI, Dina;
2011
Abstract
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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
