Some new classes of 2-fold optimal or perfect splitting authentication codes

摘要

Optimal restricted strong partially balanced t-design can be used to construct splitting authentication codes which achieve combinatorial lower bounds or information-theoretic lower bounds. In this paper, we investigate the existence of optimal restricted strong partially balanced 2-designs ORSPBD(v, k x c, 1), and show that there exists an ORSPBD(v, 2 x c, 1) for any positive integer v = v0 (mod 2c(2)) and v(0) is an element of {1 <= x <= 2c(2) : gcd(x, c) = 1 or gcd(x, c) = c} {c(2) + 1 <= x <= (c + 1)(2) : gcd(x, c) = 1 and gcd(x, 2) = 2}. Furthermore, we determine the existence of an ORSPBD(v, k x c, 1) for any integer v >= kc with (k, c) = (2, 4), (2, 5), (3, 2) or for any even integer v >= kc with (k, c) = (4, 2). As their applications, we obtain six new infinite classes of 2-fold optimal or perfect c-splitting authentication codes.