New Bounds on Parent-Identifying Codes: The Case of Multiple Parents

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 - 1 and c1(t), c2(t) are some functions of t. We also show some bounds and constructions for f3(5, q), f3(6, q), and ft(n, q) when n < s(t).

• Type: Journal
• Year: 2004
• Where: CPC
• Authors: Noga Alon, Uri Stav
• Keywords: Codewords, CPC 2004, Identifiable Parent Property, Parent