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Journals and Conferences
We give new constructions for k-regular graphs of girth 6, 8 and 12 with a small number of vertices. The key idea is to start with a generalized n-gon and delete some lines and points to decrease the valency of the incidence graph.
In this paper we construct maximal partial spreads in PG(3, q) which are a log q factor larger than the best known lower bound. For n ≥ 5 we also construct maximal partial spreads in PG(n, q) of each size between cnqn−2 log q and c′qn−1.
In this paper we characterize a sporadic non-Rédei type blocking set of PG(2, 7) having minimum cardinality, and derive an upper bound for the number of nuclei of sets in PG(2, q) having less than q + 1 points. Our methods involve polynomials over finite fields, and work mainly for planes of prime order.
We show that if a linear code admits an extension, then it necessarily admits a linear extension. There are many linear codes that are known to admit no linear extensions. Our result implies that these codes are in fact maximal. We are able to characterize maximal linear (n, k, d)q-codes as complete (weighted) (n, n − d)-arcs in PG(k−1, q). At the same time… (More)
In this paper we outline a construction method which has been used for minimal blocking sets in PG(2, q) and maximal partial line spreads in PG(n, q) and which must have a lot of more applications. We also give a survey on what is known about the spectrum of sizes of maximal partial line spreads in PG(n, q). At the end we list some more elaborate random… (More)
A three-dimensional analogue of the classical direction problem is proposed and an asymptotically sharp bound for the number of directions determined by a nonplanar set in AG(3, p), p prime, is proved. Using the terminology of permutation polynomials the main result states that if there are more than (2dp−1 6 e+1)(p+2d p−1 6 e)/2 ≈ 2p/9 pairs (a, b) ∈ Fp… (More)
Let f be a function from a finite field Fp with a prime number p of elements, to Fp. In this article we consider those functions f(X) for which there is a positive integer n > 2 √ p− 1− 11 4 with the property that f(X) , when considered as an element of Fp[X]/(X −X), has degree at most p− 2− n + i, for all i = 1, . . . , n. We prove that every line is… (More)