 
Summary: New bounds on parentidentifying codes:
The case of multiple parents
Noga Alon
Uri Stav
Abstract
Let C be a code of length n over an alphabet of q letters. A codeword y is called a descendant
of a set of t codewords {x1
, . . . , xt
} if yi {x1
i , . . . , xt
i} for all i = 1, . . . , n. A code is said to
have the Identifiable Parent Property of order t if for any word of length n that is a descendant
of at most t codewords (parents), it is possible to identify at least one of them. Let ft(n, q) be
the maximum possible cardinality of such a code. We prove that for any t, n, q, (c1(t)q)
n
s(t) <
ft(n, q) < c2(t)q
n
s(t) where s(t) = ( t
2 + 1)2
