117,299 research outputs found
Maximal curves from subcovers of the GK-curve
No full textFor every q=n3 with n a prime power greater than 2, the GK-curve is an Fqjavax.xml.bind.JAXBElement@625df14a-maximal curve that is not Fqjavax.xml.bind.JAXBElement@58c63ba-covered by the Hermitian curve. In this paper some Galois subcovers of the GK curve are investigated. Infinitely many examples of maximal curves that cannot be Galois covered by the Hermitian curve are obtained. We also describe explicit equations for some families of quotient curves of the GK-curve. In several cases, such curves provide new values in the spectrum of genera of Fqjavax.xml.bind.JAXBElement@43e74b2e-maximal curves
Algebraic geometric codes on many points from Kummer extensions
No full textFor Kummer extensions defined by ym=f(x), where f(x) is a separable polynomial over the finite field Fq, we compute the number of Weierstrass gaps at two totally ramified places. For many totally ramified places we give a criterion to find pure gaps at these points and present families of pure gaps. We then apply our results to construct n-points algebraic geometric codes with good parameters
Locally Recoverable Codes from Automorphism Group of Function Fields of Genus g ≥ 1
No full textA Locally Recoverable Code is a code such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. When we have δ non-overlapping subsets of cardinality ri that can be used to recover the missing coordinate we say that a linear code C with length n, dimension k, minimum distance d has (r1,⋯, rδ) -locality and denote by [n, k, d; r1, r2, ⋯, rδ]. In this paper we provide a new upper bound for the minimum distance of these codes. Working with a finite number of subgroups of cardinality ri+1 of the automorphism group of a function field F| Fq of genus g ≥ 1 we propose a construction of [n, k, d; r1, r2, ⋯, rδ] -codes and apply the results to some well known families of function fields
Rational functions with small value set
No full textLet q be a prime power, and let Fq be the finite field with q elements. In connection with Galois theory and algebraic curves, this paper investigates rational functions h(x)=f(x)/g(x)∈Fq(x) for which the value sets Vh={h(α)|α∈Fq∪{∞}} are relatively small. In particular, under certain circumstances, it proves that h(x) having a small value set is equivalent to the field extension Fq(x)/Fq(h(x)) being Galois
Complete permutation polynomials from exceptional polynomials
No full textWe classify complete permutation monomials of degree qn−1q−1+1 over the finite field with qn elements in odd characteristic, for n+1 a prime and (n+1)
On some Galois covers of the Suzuki and Ree curves
No full textWe investigate two families S ̃q and R ̃q of maximal curves over finite fields recently constructed by Skabelund as cyclic covers of the Suzuki and Ree curves. We show that S ̃q is not Galois covered by the Hermitian curve maximal over Fqjavax.xml.bind.JAXBElement@65baf0e, and R ̃q is not Galois covered by the Hermitian curve maximal over Fqjavax.xml.bind.JAXBElement@6d41c364. We also compute the genera of many Galois subcovers of S ̃q and R ̃q; in this way, many new values in the spectrum of genera of maximal curves are obtained. The full automorphism group of both S ̃q and R ̃q is determined
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Square Dancing with the Stars to Enhance Dynamic Hirschman Linkages?
No full textIn this Presidential Address, the author takes the reader on a reconnaissance of his life and time as a regional scientist. He points out scenery he found scintillating along the way, hoping that some may pick up the banner and chew on a few of the ideas for a while. He suggests a revisit to Albert O. Hirschman’s notion of key sectors and more empirical analysis related to Marcus Berliant’s and Masahisa Fujita’s notion of knowledge creation and transfer.Presidential Address, San Antonio, Texas, March 29, 2014 (53rd Meetings of the Southern Regional Science Association
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