A class of i.p.p. codes with efficient identification

Let C be a code of length n over a q-ary alphabet. An n-word y is called a descendant of a set of t codewords x^1,...,x^t if y_iin {x^1_i,dots,x^t_i} for all i=1,...,n. 

A code is said to have the t-identifiable parent property} (t-i. p.p.) if for any n-word y that is a descendant of at most $t$ parents it is possible to identify at least one of them. 

An explicit construction is presented of t-i.p.p. codes of rate bounded away from zero, for which identification can be accomplished with complexity poly(n).