In this paper we proceed in the way indicated by R. M. Wilson for obtaining simple difference families from finite fields [28]. We present a theorem which includes as corollaries all the known direct techniques based on Galois fields, and provides a very effective method for constructing a lot of new difference families and also new optimal optical orthogonal codes. By means of our construction—just to give an idea of its power—it has been established that the only primes p<10^5 for which the existence of a cyclic S(2, 9,p) design is undecided are 433 and 1009. Moreover we have considerably improved the lower bound on the minimum v for which an S(2, 15,v) design exists.
A powerful method for constructing difference families and optimal optical orthogonal codes / Buratti, Marco. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - 5:(1995), pp. 13-25.
A powerful method for constructing difference families and optimal optical orthogonal codes
BURATTI, Marco
1995
Abstract
In this paper we proceed in the way indicated by R. M. Wilson for obtaining simple difference families from finite fields [28]. We present a theorem which includes as corollaries all the known direct techniques based on Galois fields, and provides a very effective method for constructing a lot of new difference families and also new optimal optical orthogonal codes. By means of our construction—just to give an idea of its power—it has been established that the only primes p<10^5 for which the existence of a cyclic S(2, 9,p) design is undecided are 433 and 1009. Moreover we have considerably improved the lower bound on the minimum v for which an S(2, 15,v) design exists.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
