Title: Some results on the existence of t-all-or-nothing transforms over arbitrary alphabets,
Abstract: A $(t, s, v)$-all-or-nothing transform is a bijective mapping defined on
$s$-tuples over an alphabet of size $v$, which satisfies the condition that the
values of any $t$ input co-ordinates are completely undetermined, given only
the values of any $s-t$ output co-ordinates. The main question we address in
this paper is: for which choices of parameters does a $(t, s,
v)$-all-or-nothing transform (AONT) exist? More specifically, if we fix $t$ and
$v$, we want to determine the maximum integer $s$ such that a $(t, s, v)$-AONT
exists. We mainly concentrate on the case $t=2$ for arbitrary values of $v$,
where we obtain various necessary as well as sufficient conditions for
existence of these objects. We consider both linear and general (linear or
nonlinear) AONT. We also show some connections between AONT, orthogonal arrays
and resilient functions.