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	For Angling may be said to be so much like the Mathematicks, that it can ne'er be fully learnt; at least not so fully, but that there will still be more new experiments left for the tryal of other men that succeed us. Izaak Walton
	Dipartimento di Matematica Facoltà di Ingegneria Università degli studi di Brescia Via Valotti 9 25133 Brescia Tel. +39 030 3715739/5776 Fax. +39 030 3715745 ResearcherID: F-4066-2010

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Luca Giuzzi, DPhil (Sussex)

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Research

Topics

My research interests include:

• Finite geometry, with special regard toward
  1. Algebraic geometry techniques in finite characteristic;
  2. Computational methods for computer algebra;
  3. K-loops, fibrations and reflection structures.
• Coding theory
  1. LDPC and convolutorial codes;
  2. Algebraic decoding;
  3. Codes arising from incidence structures;
  4. Algebraic Geometry Codes.
• Cryptography:
  1. Public key cryptography and (hyper-)elliptic curves;
  2. Information theory;
  3. Private key cryptosystem design.

Preprints and papers

Theses

1. L. Giuzzi, Gruppi di Frobenius e strutture geometriche associate, Tesi di Laurea (Advisor: Prof. S. Pianta) 1996.
2. L. Giuzzi, Hermitian varieties over finite fields, DPhil thesis (Supervisor: Prof. J.W.P. Hirschfeld) 2000.

Books

1. L. Giuzzi, Codici correttori, Unitext Springer Verlag n. 27 (2006), ISBN: 88-470-0539-6.

Accepted papers

1. L. Giuzzi, Collineation groups of the intersection of two classical unitals, J. Comb. Des. 9: 445-459 (2001), ISSN: 1063-8539, doi:10.1002/jcd.1023
2. L. Giuzzi, H. Karzel, Co-Minkowski spaces, their reflection structure and K-loops, Discrete Math. 255: 161-179 (2002), ISSN: 0012-365X, doi:10.1016/S0012-365X(01)00396-X
3. L. Giuzzi, A characterisation of classical unitals, J. Geom. 74: 86-89 (2002), ISSN: 0047-2468, doi:10.1007/PL00012541
4. L. Giuzzi, G. Korchmáros, Ovoids of the Hermitian Surface in Odd Characteristic, Adv. Geom Special Issue: S49-S58 (2003), ISSN: 1615-715X.
5. L. Giuzzi, On the intersection of Hermitian surfaces, J. Geom. 85: 49-60 (2006), ISSN: 0047-2468, doi:10.1007/s00022-006-0042-4
6. L. Giuzzi, A geometric construction for some ovoids of the Hermitian Surface, Results in Mathematics 49: 81-88 (2006), ISSN: 1422-6383, doi:10.1007/s00025-006-0210-8
7. A. Aguglia, L. Giuzzi, Orthogonal arrays from Hermitian varieties (arXiv:0705.3590), Innovations in Incidence Geometry 5: 129-144 (2007), ISSN: 1781-6475.
8. A. Aguglia, L. Giuzzi, An algorithm for constructing some maximal arcs in \(\mathrm{PG}(2,q^2)\) (arxiv:math/0611466), Results in Mathematics 52 no. 1-2: 17-33 (2008), ISSN: 1422-6383, doi:10.1007/s00025-007-0268-y
9. A. Aguglia, L. Giuzzi, Construction of a 3-Dimensional MDS code (arxiv:0708.1558), Contributions to Discrete Mathematics 3 no. 1: 39-46 (2007), ISSN: 1715-0868.
10. A. Aguglia, L. Giuzzi, G. Korchmáros, Algebraic curves and maximal arcs (arxiv:math/0702770), Journal of Algebraic Combinatorics 28: 531-544 (2008), ISSN: 0925-9899, doi:10.1007/s10801-008-0122-7
11. A. Aguglia, L. Giuzzi, On the non-existence of some inherited ovals in Moulton planes of even order(arxiv:0803.1597), Electronic Journal of Combinatorics 15(1): N37 (2008)
12. L. Giuzzi, A. Sonnino, LDPC codes from Singer cycles (arxiv:0709.2813), Discrete Applied Mathematics 157: 1723-1728 (2009), ISSN: 0166-218X, doi:10.1016/j.dam.2009.01.013
13. A. Aguglia, L. Giuzzi, G. Korchmáros, Construction of unitals in Desarguesian planes (arXiv:0810.2233), Discrete Math. 310 (22): 3162-3167 (2010), ISSN: 0012-365X, doi:10.1016/j.disc.2009.06.023
14. A. Benini, L. Giuzzi, A. Pasotti, Down-linking \((K_v,\Gamma)\)-designs to \(P_3\)-designs, Utilitas Mathematica, in press, ISSN: 0315-3681. (arXiv:1004.4127)
15. L. Giuzzi, A. Pasotti, Sampling complete graphs (arXiv:0907.3199), to appear on Discrete Math. doi:10.1016/j.disc.2011.02.034
16. L. Giuzzi, G. Korchmáros, Unitals in \(PG(2,q^2)\) with a large 2-point stabiliser (arXiv:1009.6109), to appear on Discrete Math. doi:10.1016/j.disc.2011.03.017

Preprints

Most of my old preprints might be found here; some other notes on mathematics are available on this page.

The following are current preprints:

1. A. Benini, L. Giuzzi, A. Pasotti, New results on path-decompositions and their down-links, (arXiv:1106.1095).
2. L. Giuzzi, V. Pepe, Families of twisted tensor product codes, (arXiv:1107.1066).

Reports

1. L. Giuzzi, Looking for ovoids of the Hermitian surface: a computational approach (2004).

Lecture notes

1. L.Giuzzi, lecture notes of the course Algebraic geometry over a field of positive characteristic, given by J.W.P. Hirschfeld (1998).
2. L.Giuzzi, A. Sonnino, Alcune note introduttive sulla crittografia (2005).

Patents

1. L. Giuzzi, G. Korchmáros, A. Sonnino, Perfezionamenti nella crittografia a chiave pubblica basata su curve ellittiche, patent no. 0001379714, 30 August 2010

Links

Here there are some links to research databases wherein I appear:

• Google Scholar
• Microsoft Academic Seach
• arXiv

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