Discrete mathematics, ISSN 0012-365X, 2018, Volume 341, Issue 8, pp. 2121 - 2130

In this paper we investigate light dual multinets labeled by a finite group in the projective plane PG(2,K) defined over a field K. We present two classes of...

Quasigroup | Projective plane | 3-net | Multinet | Line arrangement | Embedding | Latin square | MATHEMATICS | NETS | PENCIL | CURVES | Mathematics - Combinatorics

Quasigroup | Projective plane | 3-net | Multinet | Line arrangement | Embedding | Latin square | MATHEMATICS | NETS | PENCIL | CURVES | Mathematics - Combinatorics

Journal Article

Journal of combinatorial theory. Series A, ISSN 0097-3165, 2019, Volume 165, pp. 408 - 439

We present a new method for the study of hemisystems of the Hermitian surface U3 of PG(3,q2). The basic idea is to represent generator-sets of U3 by means of a...

Hermitian surface | Maximal curves | Hemisystem | MATHEMATICS | Mathematics - Combinatorics

Hermitian surface | Maximal curves | Hemisystem | MATHEMATICS | Mathematics - Combinatorics

Journal Article

2008, STU - Student edition, Princeton series in applied mathematics, ISBN 9780691096797, xx, 696

This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental...

Mathematics | Curves, Algebraic | Finite fields (Algebra)

Mathematics | Curves, Algebraic | Finite fields (Algebra)

Book

ALGEBRA & NUMBER THEORY, ISSN 1937-0652, 2019, Volume 13, Issue 1, pp. 1 - 18

Let X be an ordinary (projective, geometrically irreducible, nonsingular) algebraic curve of genus g (X) >= 2 defined over an algebraically closed field K of...

MATHEMATICS | algebraic curves | positive characteristic | algebraic function fields | automorphism groups | FUNCTION-FIELDS

MATHEMATICS | algebraic curves | positive characteristic | algebraic function fields | automorphism groups | FUNCTION-FIELDS

Journal Article

Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 05/2013, Volume 40, pp. 135 - 138

We fill up a gap in Hennʼs proof concerning large automorphism groups of function fields of degree 1 over an algebraically closed field of positive...

automorphism groups | algebraic function fields | Algebraic curves | Automorphism groups | Algebraic function fields

automorphism groups | algebraic function fields | Algebraic curves | Automorphism groups | Algebraic function fields

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 6/2014, Volume 39, Issue 4, pp. 939 - 966

...J Algebr Comb (2014) 39:939–966 DOI 10.1007/s10801-013-0474-5 3-Nets realizing a group in a projective plane Gábor Korchmáros · Gábor P . Nagy · Nicola Pace...

Dual 3-net | Convex and Discrete Geometry | Projective plane | 3-Net | Embedding | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Cubic curve | MATHEMATICS

Dual 3-net | Convex and Discrete Geometry | Projective plane | 3-Net | Embedding | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Cubic curve | MATHEMATICS

Journal Article

Mathematische annalen, ISSN 1432-1807, 2008, Volume 343, Issue 1, pp. 229 - 245

...Math. Ann. (2009) 343:229–245 DOI 10.1007/s00208-008-0270-z Mathematische Annalen A new family of maximal curves over a ﬁnite ﬁeld Massimo Giulietti · Gábor...

11G20 | Mathematics, general | Mathematics | FIBER PRODUCTS | MATHEMATICS | RATIONAL-POINTS | ALGEBRAIC FUNCTION | NUMBER | AUTOMORPHISM GROUP | GENUS | DELIGNE-LUSZTIG CURVE | KUMMER COVERS | SUBFIELDS | GENERALIZED HAMMING WEIGHTS | Cryptography

11G20 | Mathematics, general | Mathematics | FIBER PRODUCTS | MATHEMATICS | RATIONAL-POINTS | ALGEBRAIC FUNCTION | NUMBER | AUTOMORPHISM GROUP | GENUS | DELIGNE-LUSZTIG CURVE | KUMMER COVERS | SUBFIELDS | GENERALIZED HAMMING WEIGHTS | Cryptography

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2013, Volume 56, Issue 7, pp. 1449 - 1455

Korchmaros and Nagy [Hermitian codes from higher degree places. J Pure Appl Algebra, doi： 10. 1016/j.jpaa.2013.04.002, 2013] computed the Weierstrass gap...

最小距离 | 代数几何 | 差分码 | 改进设计 | 下界 | 埃尔米特 | 维尔斯特拉斯 | DOI | 11T71 | 94B27 | AG code | Mathematics | Applications of Mathematics | 11G20 | 14H55 | Weierstrass gap | Hermitian curve | MATHEMATICS | MATHEMATICS, APPLIED | GOPPA CODES | WEIERSTRASS SEMIGROUP | IMPROVEMENTS | GAPS | PAIR | Algebra | Integers | Lower bounds | Computation | Mathematical analysis | China | Group theory | Mathematical models | Series (mathematics) | Astronomy

最小距离 | 代数几何 | 差分码 | 改进设计 | 下界 | 埃尔米特 | 维尔斯特拉斯 | DOI | 11T71 | 94B27 | AG code | Mathematics | Applications of Mathematics | 11G20 | 14H55 | Weierstrass gap | Hermitian curve | MATHEMATICS | MATHEMATICS, APPLIED | GOPPA CODES | WEIERSTRASS SEMIGROUP | IMPROVEMENTS | GAPS | PAIR | Algebra | Integers | Lower bounds | Computation | Mathematical analysis | China | Group theory | Mathematical models | Series (mathematics) | Astronomy

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 7/2013, Volume 68, Issue 1, pp. 73 - 79

...Des. Codes Cryptogr. (2013) 68:73–79 DOI 10.1007/s10623-012-9619-0 Transitive A 6 -invariant k-arcs in PG ( 2,q ) Massimo Giulietti · Gábor Korchmáros...

Information and Communication, Circuits | Data Structures, Cryptology and Information Theory | k -arcs | Discrete Mathematics in Computer Science | Data Encryption | A 6 | Coding and Information Theory | Finite desarguesian planes | Mathematics | 51E21 | Combinatorics | k-arcs

Information and Communication, Circuits | Data Structures, Cryptology and Information Theory | k -arcs | Discrete Mathematics in Computer Science | Data Encryption | A 6 | Coding and Information Theory | Finite desarguesian planes | Mathematics | 51E21 | Combinatorics | k-arcs

Journal Article

09/2019

A group $G$ has a Frobenius graphical representation (GFR) if there is a simple graph $\varGamma$ whose full automorphism group is isomorphic to $G$ and it...

Mathematics - Group Theory

Mathematics - Group Theory

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 6/2016, Volume 79, Issue 3, pp. 443 - 449

...Des. Codes Cryptogr. (2016) 79:443–449 DOI 10.1007/s10623-016-0176-9 3-Nets realizing a diassociative loop in a projective plane Gábor Korchmáros 1 · Gábor P...

Information and Communication, Circuits | 20N05 | Data Encryption | 3-Net | Mathematics | Diassociative loop | Latin square | 51E99 | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Projective plane | Coding and Information Theory | Transversal design | Combinatorics

Information and Communication, Circuits | 20N05 | Data Encryption | 3-Net | Mathematics | Diassociative loop | Latin square | 51E99 | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Projective plane | Coding and Information Theory | Transversal design | Combinatorics

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 7/2014, Volume 72, Issue 1, pp. 53 - 75

...Des. Codes Cryptogr. (2014) 72:53–75 DOI 10.1007/s10623-013-9806-7 Coset intersection of irreducible plane cubics Gábor Korchmáros · Nicola Pace Received: 29...

Information and Communication, Circuits | Abelian group | Configuration | Data Encryption | 05B30 | 14H52 | Mathematics | Data Structures, Cryptology and Information Theory | Coset | Discrete Mathematics in Computer Science | Projective plane | Coding and Information Theory | Plane cubic curves | Combinatorics | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Information and Communication, Circuits | Abelian group | Configuration | Data Encryption | 05B30 | 14H52 | Mathematics | Data Structures, Cryptology and Information Theory | Coset | Discrete Mathematics in Computer Science | Projective plane | Coding and Information Theory | Plane cubic curves | Combinatorics | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 7/2013, Volume 68, Issue 1, pp. 61 - 72

...Des. Codes Cryptogr. (2013) 68:61–72 DOI 10.1007/s10623-012-9630-5 Arcs in AG(2,q )determining few directions Massimo Giulietti · Gábor Korchmáros Received: 30...

Information and Communication, Circuits | Data Structures, Cryptology and Information Theory | Desarguesian net | Discrete Mathematics in Computer Science | Data Encryption | Projective plane | Complete arc | Coding and Information Theory | Mathematics | 51E21 | Combinatorics | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Information and Communication, Circuits | Data Structures, Cryptology and Information Theory | Desarguesian net | Discrete Mathematics in Computer Science | Data Encryption | Projective plane | Complete arc | Coding and Information Theory | Mathematics | 51E21 | Combinatorics | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 7/2012, Volume 64, Issue 1, pp. 33 - 46

...Des. Codes Cryptogr. (2012) 64:33–46 DOI 10.1007/s10623-011-9532-y 42-arcs in PG (2, q) left invariant by PSL (2, 7) Lucia Indaco · Gábor Korchmáros Received...

Information and Communication, Circuits | Data Structures, Cryptology and Information Theory | 20G40 | k -arcs | Discrete Mathematics in Computer Science | Data Encryption | Coding and Information Theory | Mathematics | Finite desarguesian plane | Combinatorics | PSL (2, 7) | 51E15 | k-arcs | PSL(2, 7) | OVALS | MATHEMATICS, APPLIED | NUMBER | PROJECTIVE-PLANES | CURVES | ORDER | PSL(2,7) | FINITE-FIELD | COMPUTER SCIENCE, THEORY & METHODS | POINTS | ARCS

Information and Communication, Circuits | Data Structures, Cryptology and Information Theory | 20G40 | k -arcs | Discrete Mathematics in Computer Science | Data Encryption | Coding and Information Theory | Mathematics | Finite desarguesian plane | Combinatorics | PSL (2, 7) | 51E15 | k-arcs | PSL(2, 7) | OVALS | MATHEMATICS, APPLIED | NUMBER | PROJECTIVE-PLANES | CURVES | ORDER | PSL(2,7) | FINITE-FIELD | COMPUTER SCIENCE, THEORY & METHODS | POINTS | ARCS

Journal Article

Advances in mathematics (New York. 1965), ISSN 0001-8708, 2019, Volume 349, pp. 162 - 211

Let X be a (projective, geometrically irreducible, non-singular) algebraic curve of genus g≥2 defined over an algebraically closed field K of odd...

Automorphism groups | Algebraic curves | Positive characteristic | FINITE SIMPLE-GROUPS | MATHEMATICS | NUMBER | SUBGROUPS

Automorphism groups | Algebraic curves | Positive characteristic | FINITE SIMPLE-GROUPS | MATHEMATICS | NUMBER | SUBGROUPS

Journal Article

Journal of Geometry, ISSN 0047-2468, 4/2014, Volume 105, Issue 1, pp. 43 - 55

Basic properties of polygons in Euclidean space and some related regularity questions were explored in the first part of the Nineteen century. Systematic...

Geometry | Primary 51M04 | Secondary 51M05 | polygon | Mathematics | Euclidean space | Equilateral | Algebra

Geometry | Primary 51M04 | Secondary 51M05 | polygon | Mathematics | Euclidean space | Equilateral | Algebra

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 7/2012, Volume 64, Issue 1, pp. 3 - 15

...Des. Codes Cryptogr. (2012) 64:3–15 DOI 10.1007/s10623-011-9562-5 Projective k-arcs and 2-level secret-sharing schemes Gábor Korchmáros · Valentino Lanzone...

Secret-sharing scheme | Information and Communication, Circuits | Data Encryption | Mathematics | Data Structures, Cryptology and Information Theory | Sharply focused arc | Discrete Mathematics in Computer Science | k -arc | Oval | Primary: 51E20 | Coding and Information Theory | Combinatorics | Hyperfocused arc | 94A99 | Equifocused arc | Secondary: 05B25 | k-arc | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Secret-sharing scheme | Information and Communication, Circuits | Data Encryption | Mathematics | Data Structures, Cryptology and Information Theory | Sharply focused arc | Discrete Mathematics in Computer Science | k -arc | Oval | Primary: 51E20 | Coding and Information Theory | Combinatorics | Hyperfocused arc | 94A99 | Equifocused arc | Secondary: 05B25 | k-arc | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

18.
Full Text
Large odd prime power order automorphism groups of algebraic curves in any characteristic

10/2018

Let $\mathcal{X}$ be a (projective, geometrically irreducible, nonsingular) algebraic curve of genus $g \ge 2$ defined over an algebraically closed field...

Mathematics - Algebraic Geometry

Mathematics - Algebraic Geometry

Journal Article

19.
Full Text
Large odd prime power order automorphism groups of algebraic curves in any characteristic

Journal of algebra, ISSN 0021-8693, 2020, Volume 547, pp. 312 - 344

Let X be a (projective, geometrically irreducible, nonsingular) algebraic curve of genus g≥2 defined over an algebraically closed field K of odd characteristic...

Automorphism groups | Algebraic curves | Positive characteristic | Algebraic function fields | MATHEMATICS | FINITE P-GROUPS

Automorphism groups | Algebraic curves | Positive characteristic | Algebraic function fields | MATHEMATICS | FINITE P-GROUPS

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 5/2010, Volume 55, Issue 2, pp. 285 - 296

...Des. Codes Cryptogr. (2010) 55:285–296 DOI 10.1007/s10623-009-9343-6 Inﬁnite family of large complete arcs in PG(2, q n ), with q odd and n > 1o d d Gábor...

Information and Communication, Circuits | Data Structures, Cryptology and Information Theory | Arc | Discrete Mathematics in Computer Science | Data Encryption | Projective plane | Collineation group | Coding and Information Theory | Mathematics | 51E21 | Combinatorics | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | PLANE ARCS

Information and Communication, Circuits | Data Structures, Cryptology and Information Theory | Arc | Discrete Mathematics in Computer Science | Data Encryption | Projective plane | Collineation group | Coding and Information Theory | Mathematics | 51E21 | Combinatorics | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | PLANE ARCS

Journal Article

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