  In this paper, we study the signature codes for weighted binary adder channel
(WbAC) and collusion-resistant multimedia fingerprinting. Let $A(n,t)$ denote
the maximum cardinality of a $t$-signature code of length $n$, and $A(n,w,t)$
denote the maximum cardinality of a $t$-signature code of length $n$ and
constant weight $w$. First, we derive asymptotic and general upper bounds of
$A(n,t)$ by relating signature codes to $B_t$ codes and bipartite graphs with
large girth respectively, and also show the upper bounds are tight for certain
cases. Second, we determine the exact values of $A(n,2,2)$ and $A(n,3,2)$ for
infinitely many $n$ by connecting signature codes with $C_4$-free graphs and
union-free families, respectively. Third, we provide two explicit constructions
for $t$-signature codes which have efficient decoding algorithms and
applications to two-level signature codes. Furthermore, we show from the
geometric viewpoint that there does not exist any binary code with complete
traceability for noisy WbAC and multimedia fingerprinting. A new type of
signature codes with a weaker requirement than complete traceability is
introduced for the noisy scenario.
