Showing papers by "J. W. P. Hirschfeld published in 2001"
01 Jan 2001
TL;DR: In this paper, the authors updated the 1998 survey on the packing problem, up to 1995, and showed that considerable progress has been made on different kinds of subconfigurations over the last few decades.
Abstract: This article updates the authors’ 1998 survey [134] on the same theme that was written for the Bose Memorial Conference (Colorado, June 7–11, 1995). That article contained the principal results on the packing problem, up to 1995. Since then, considerable progress has been made on different kinds of subconfigurations.
236 citations
TL;DR: In this article, the Stohr-Voloch approach was used to obtain a new bound for the number of solutions in (F q ) 2 of an equation f ( X, Y ) = 0, where f (X, Y) is an irreducible polynomial with coefficients in a finite field F q.
Abstract: The Stohr–Voloch approach is used to obtain a new bound for the number of solutions in ( F q ) 2 of an equation f ( X , Y ) = 0, where f ( X , Y ) is an absolutely irreducible polynomial with coefficients in a finite field F q .
8 citations
01 Jan 2001
TL;DR: In this paper, the algebraic curve associated to an arc in PG(2, q), with q odd, is examined using both properties of the curve itself as well as properties of arc.
Abstract: The algebraic curve associated to an arc in PG(2, q), with q odd, is examined using both properties of the curve itself as well as properties of the arc. The key case of (q − 1)-arcs means that the behaviour of the associated sextic curves needs to be studied. The case of PG(2, 13) is examined in detail. There is a geometric bijection between 12-arcs and their duals. The latter lead to optimal sextic curves; the former lead to sextics whose set of rational points make them ‘look like’ quartics.
3 citations