TY - JOUR

T1 - New bounds on parent-identifying codes

T2 - The case of multiple parents

AU - Alon, Noga

AU - Stav, Uri

N1 - Funding Information:
SK wishes to thank Indian National Science Academy for grant of its Honorary Scientistship to him. Facilities provided by NIPGR are also gratefully acknowledged.

PY - 2004/11

Y1 - 2004/11

N2 - 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, . . . ,x t} if yi, ∈ {xi1, . . . ,x it} 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), c 2(t) are some functions of t. We also show some bounds and constructions for f3(5,q). f3(6,q), and f t,(n,q) when n < s(t).

AB - 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, . . . ,x t} if yi, ∈ {xi1, . . . ,x it} 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), c 2(t) are some functions of t. We also show some bounds and constructions for f3(5,q). f3(6,q), and f t,(n,q) when n < s(t).

UR - http://www.scopus.com/inward/record.url?scp=9744257021&partnerID=8YFLogxK

U2 - 10.1017/S0963548304006388

DO - 10.1017/S0963548304006388

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AN - SCOPUS:9744257021

SN - 0963-5483

VL - 13

SP - 795

EP - 807

JO - Combinatorics Probability and Computing

JF - Combinatorics Probability and Computing

IS - 6

ER -