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- W1992185324 abstract "Let C be a code of length n over an alphabet of q letters. For a pair of integers 2⩽ t < u , C is ( t , u )-hashing if for any two subsets T , U ⊂ C , satisfying T ⊂ U , | T |= t , | U |= u , there is a coordinate 1⩽ i ⩽ n such that for any x ∈ T , y ∈ U − x , x and y differ in the i th coordinate. This definition, generalizing the standard notion of a t -hashing family, is motivated by an application in designing the so-called parent identifying codes, used in digital fingerprinting. In this paper, we provide lower and upper bounds on the best possible rate of ( t , u )-hashing families for fixed t , u and growing n . We also describe an explicit construction of ( t , u )-hashing families. The obtained lower bound on the rate of ( t , u )-hashing families is applied to get a new lower bound on the rate of t -parent identifying codes." @default.
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- W1992185324 date "2003-10-01" @default.
- W1992185324 modified "2023-09-30" @default.
- W1992185324 title "Generalized hashing and parent-identifying codes" @default.
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- W1992185324 doi "https://doi.org/10.1016/j.jcta.2003.08.001" @default.
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