Search results for: Kit-Ho Mak

Items from 1 to 6 out of 6 results

article

On the correlation of families of pseudorandom sequences of k symbols

Kit-Ho Mak, Alexandru Zaharescu

Acta Arithmetica > 2016 > 174 > 3 > 199-215

In an earlier paper Gyarmati introduced the notion of f-correlation for families of binary pseudorandom sequences as a measure of randomness in the family. In this paper we generalize the f-correlation to families of pseudorandom sequences of k symbols and study its properties.

article

More constructions of pseudorandom lattices of $$k$$ k symbols

Kit-Ho Mak

Monatshefte für Mathematik > 2015 > 177 > 2 > 307-323

We define the pseudorandom lattice of $$k$$ k symbols, and present some new constructions of families of such lattices, which generalize several previous constructions for the pseudorandom binary lattices. These lattices can also be regarded as a high dimensional analogue of some pseudorandom sequences of $$k$$ k symbols.

article

On the distribution of the number of points on a family of curves over finite fields

Kit-Ho Mak, Alexandru Zaharescu

Journal of Number Theory > 2014 > 140 > Complete > 277-298

Let p be a large prime, ℓ⩾2 be a positive integer, m⩾2 be an integer relatively prime to ℓ and P(x)∈Fp[x] be a polynomial which is not a complete ℓ′-th power for any ℓ′ for which GCD(ℓ′,ℓ)=1. Let C be the curve defined by the equation yℓ=P(x), and take the points on C to lie in the rectangle [0,p−1]2. In this paper, we study the distribution of the number of points on C inside small rectangles among...

article

The distribution of points on curves over finite fields in some small rectangles

Kit-Ho Mak

Monatshefte für Mathematik > 2014 > 174 > 4 > 577-586

Let $$p$$ p be a prime. We study the distribution of points on a class of curves $$C$$ C over $$\mathbb{F }_p$$ F p inside very small rectangles $$\mathcal{B }$$ B for which the Weil bound fails to give nontrivial information. In particular, we show that the distribution of points on $$C$$ C over long rectangles is Gaussian.

article

More constructions of pseudorandom sequences of k symbols

Kit-Ho Mak

Finite Fields and Their Applications > 2014 > 25 > Complete > 222-233

We present some new constructions of families of pseudorandom sequences of k symbols, which generalize several previous constructions for the binary case.

article

On maximal curves which are not Galois subcovers of the Hermitian curve

Iwan Duursma, Kit-Ho Mak

Bulletin of the Brazilian Mathematical Society, New Series > 2012 > 43 > 3 > 453-465

We show that the generalized Giulietti-Korchmáros curve defined over $$\mathbb{F}_{q^{2n} }$$ , for n ≥ 3 odd and q ≥ 3, is not a Galois subcover of the Hermitian curve over $$\mathbb{F}_{q^{2n} }$$ . This answers a question raised by Garcia, Güneri and Stichtenoth.

INFONA - science communication portal

Search results for: Kit-Ho Mak

On the correlation of families of pseudorandom sequences of k symbols

More constructions of pseudorandom lattices of $$k$$ k symbols

On the distribution of the number of points on a family of curves over finite fields

The distribution of points on curves over finite fields in some small rectangles

More constructions of pseudorandom sequences of k symbols

On maximal curves which are not Galois subcovers of the Hermitian curve

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INFONA - science communication portal

Search results for: Kit-Ho Mak

On the correlation of families of pseudorandom sequences of k symbols

More constructions of pseudorandom lattices of $$k$$ k symbols

On the distribution of the number of points on a family of curves over finite fields

The distribution of points on curves over finite fields in some small rectangles

More constructions of pseudorandom sequences of k symbols

On maximal curves which are not Galois subcovers of the Hermitian curve

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