Incomplete (rq-q+r- ɛ , r)-arcs and minimal {ℓ,t}-Blocking set in PG(2,q)

New Large (n, r)-arcs in PG(2, q)

An $(n, r)$-arc is a set of $n$ points of a projective plane such that some $r$, but no $r+1$ of them, are collinear. The maximum size of an $(n, r)$-arc in  $PG(2, q)$ is denoted by $m_r(2,q)$.  In this paper we present  a new $(184,12)$-arc in PG$(2,17),$  a new $(244,14)$-arc and a new $(267,15$)-arc in $PG(2,19).$

On the largest minimal blocking set in PG(𝔽8)

Incomplete Pivoted QR-based Dimensionality Reduction

High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to ‘curse of dimensionality’ phenomenon. Therefore, dimensionality reduction methods are applied to the data prior to its analysis. Many of these methods are based on principal com...

Multiple blocking sets and arcs in finite planes

This paper contains two main results relating to the size of a multiple blocking set in PG(2, q). The first gives a very general lower bound, the second a much better lower bound for prime planes. The latter is used to consider maximum sizes of (k, n)-arcs in PG(2, 11) and PG(2, 13), some of which are determined. In addition, a summary is given of the value of mn(2, q) for q ≤ 13.

Factoring N=p^rq^s for Large r and s

Boneh et al. showed at Crypto 99 that moduli of the form N = pq can be factored in polynomial time when r ' log p. Their algorithm is based on Coppersmith’s technique for finding small roots of polynomial equations. In this paper we show that N = pq can also be factored in polynomial time when r or s is at least (log p); therefore we identify a new class of integers that can be efficiently fact...