Some recursive constructions for perfect hash families

Atıcı, Mustafa; Magliveras, Spyros S.; Stinson, Douglas R.; Wen, Wei

doi:10.1002/(sici)1520-6610(1996)4:5<353::aid-jcd4>3.0.co;2-e

Cited by 52 publications

(53 citation statements)

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“…Further, the tuples (x + yh 1 + zh 2 1 , x + yh 2 + zh 2 2 , x + yh 3 + zh 2 3 , x + yh 1 + zh 2 1 + i), for any x, y ∈ {0, 1, 2} and for i, z ∈ {1, 2}, are covered in G 3 . Finally, the tuples (x + yh 1 + zh 2 1 , x + yh 2 + zh 2 2 , x + yh 3 + zh 2 3 , x + yh 1 + zh 2 1 ), where x, y ∈ {0, 1, 2} and z ∈ {1, 2}, are covered in G 5 . Hence, all 4-tuples are covered.…”

Section: Specializations When = V =mentioning

confidence: 99%

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Roux-type constructions for covering arrays of strengths three and four

et al. 2006

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A covering array CA(N; t, k, v) is an N × k array such that every N × t sub-array contains all t-tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t-sets of component interactions. Recursive constructions for covering arrays of strengths 3 and 4 are developed, generalizing many "Roux-type" constructions. A numerical comparison with current construction techniques is given through existence tables for covering arrays.

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Section: Specializations When = V =mentioning

confidence: 99%

“…, v − 1. Let A (2) be an OA(v 2 ; 2, v, v) which is also a CA(v 2 ; 2, v, v). Such an array exists by Theorem 2.1.…”

Section: Specializations When = V >mentioning

confidence: 99%

Roux-type constructions for covering arrays of strengths three and four

et al. 2006

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“…There are numerous constructions for perfect hash families and their variants that are effective in constructing covering arrays; see, for example, [1,24,47,53] for recursive constructions. Here we focus on direct constructions using codes.…”

Section: Hash Families Packings and Codesmentioning

confidence: 99%

“…Lemma 4.9.A linear TD(q + 1, q) contains an ( , {0, 1, 2}, a1 2 x 1 y )-thwart for 0 ≤ a−2 ≤ max(0, q−2−4 x 2 −2xy− y 2 ) whenever x, y ≥ 0 and x+y ≤ q+2 2 .Proof. Form the TD(q + 1, q) containing a ( q+2 {0, 1, 2}, 2, .…”

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confidence: 99%

Constructing heterogeneous hash families by puncturing linear transversal designs

Colbourn

2011

J. Geom.

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Constructions that use hash families to select columns from small covering arrays in order to construct larger ones can exploit heterogeneity in the numbers of symbols in the rows of the hash family. For specific distributions of numbers of symbols, the efficacy of the construction is improved by accommodating more columns in the hash family. Known constructions of such heterogeneous hash families employ finite geometries and their associated transversal designs. Using thwarts in transversal designs, specific constructions of heterogeneous hash families are developed, and some open questions are posed.

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“…That is the number of locks is 11 5 = 462 and the number of keys carried by each scientist is 10 5 = 252. Now, by using GCA, we are able to give a better solution, for which we need to employ the following algorithm for perfect hash families due to Aciti et al [4].…”

Section: Generalised Cumulative Arrays From Perfect Hash Familiesmentioning

confidence: 99%

Generalised Cumulative Arrays in Secret Sharing

et al. 2006

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Cumulative arrays have played an important role in the early development of the secret sharing theory. They have not been subject to extensive study so far, as the secret sharing schemes built on them generally result in much larger sizes of shares, when compared with other conventional approaches. Recent works in threshold cryptography show that cumulative arrays may be the appropriate building blocks in non-homomorphic threshold cryptosystems where the conventional secret sharing methods are generally of no use. In this paper we study several extensions of cumulative arrays and show that some of these extensions significantly improve the performance of conventional cumulative arrays. In particular, we derive bounds on generalised cumulative arrays and show that the constructions based on perfect hash families are asymptotically optimal. We also introduce the concept of ramp perfect hash families as a generalisation of perfect hash families for the study of ramp secret sharing schemes and ramp cumulative arrays.

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Some recursive constructions for perfect hash families

Cited by 52 publications

References 0 publications

Roux-type constructions for covering arrays of strengths three and four

Roux-type constructions for covering arrays of strengths three and four

Constructing heterogeneous hash families by puncturing linear transversal designs

Generalised Cumulative Arrays in Secret Sharing

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