Explicit Constructions of Perfect Hash Families from Algebraic Curves over Finite Fields
نویسندگان
چکیده
منابع مشابه
Explicit constructions for perfect hash families
Let k, v, t be integers such that k ≥ v ≥ t ≥ 2. A perfect hash family PHF(N ; k, v, t) can be defined as an N × k array with entries from a set of v symbols such that every N× t subarray contains at least one row having distinct symbols. Perfect hash families have been studied by over 20 years and they find a wide range of applications in computer sciences and in cryptography. In this paper we...
متن کاملSome Recursive Constructions for Perfect Hash Families
An (n; m; w)-perfect hash family is a set of functions F such that there exists at least one f 2 F such that fj X is one-to-one. Perfect hash families have been extensively studied by computer scientists for over 15 years, mainly from the point of view of constructing eecient algorithms. In this paper, we study perfect hash families from a com-binatorial viewpoint, and describe some new recursi...
متن کاملWorkshop on Algebraic Curves Over Finite Fields
Let L(t) = 1+a1t+ · · ·+a2gt be the numerator of the zeta function of an algebraic curve C defined over the finite field Fq of genus g. We show that the coefficients ar of L(t) satisfy certain inequalities. Conversely, for any integers a1, . . . , am satisfying these inequalities and all sufficiently large integers g there exist curves of genus g, whose L-polynomial satisfies the following cong...
متن کاملQuasi-Perfect Lee Codes from Quadratic Curves over Finite Fields
Golomb and Welch conjectured in 1970 that there only exist perfect Lee codes for radius t = 1 or dimension n = 1, 2. It is admitted that the existence and the construction of quasi-perfect Lee codes have to be studied since they are the best alternative to the perfect codes. In this paper we firstly highlight the relationships between subset sums, Cayley graphs, and Lee linear codes and present...
متن کاملNew Infinite Families of 3-Designs from Algebraic Curves of Higher Genus over Finite Fields
In this paper, we give a simple method for computing the stabilizer subgroup of D(f) = {α ∈ Fq | there is a β ∈ Fq such that βn = f(α)} in PSL2(Fq), where q is a large odd prime power, n is a positive integer dividing q − 1 greater than 1, and f(x) ∈ Fq[x]. As an application, we construct new infinite families of 3-designs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2001
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3068