Two-character sets, Veronese varieties and Grassmannian of lines

Authors: Cossidente A., Marino G.

Source: Ricerche di Matematica. 74:207-218

Subject Terms: Conic, Combinatorial codes, Conic, Grassmannian, Veronese variety, Grassmannian, conic, Combinatorial structures in finite projective spaces, 0102 computer and information sciences, Veronese variet, 0101 mathematics, Veronese variety, 01 natural sciences, Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: https://hdl.handle.net/11588/959324

Erratum: Mumford representation and Riemann-Roch space of a divisor on a hyperelliptic curve

Authors: Giuseppe Filippone

Source: Cryptography and Communications. 17:307-309

Subject Terms: hyperelliptic curves, Riemann-Roch space, Special divisors on curves (gonality, Brill-Noether theory), Goppa codes, Applications to coding theory and cryptography of arithmetic geometry, Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

The minimum distance of a parameterized code over an even cycle

Authors: Camps-Moreno, Eduardo, Neves, Jorge, Sarmiento, Eliseo

Source: Finite Fields and Their Applications. 106:102630

Subject Terms: parameterized linear codes, FOS: Computer and information sciences, Computer Science - Information Theory, Information Theory (cs.IT), Algebraic coding theory, cryptography (number-theoretic aspects), Applications to coding theory and cryptography of arithmetic geometry, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Finite ground fields in algebraic geometry, Mathematics - Algebraic Geometry, FOS: Mathematics, minimum distance, Algebraic Geometry (math.AG), Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: http://arxiv.org/abs/2403.05445

There are no good infinite families of toric codes

Authors: Jason P. Bell, Sean Monahan, Matthew Satriano, Karen Situ, Zheng Xie

Source: Journal of Combinatorial Theory, Series A. 213:106009

Subject Terms: FOS: Computer and information sciences, 14G50, 14M25, 11B30, 94B05, toric codes, Lovasz local lemma, Computer Science - Information Theory, Information Theory (cs.IT), Applications to coding theory and cryptography of arithmetic geometry, Mathematics - Algebraic Geometry, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Szemerédi's theorem, Algebraic Geometry (math.AG), Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: http://arxiv.org/abs/2406.00243
https://zbmath.org/8017441
https://doi.org/10.1016/j.jcta.2025.106009

On a relation between GAG codes and AG codes

Authors: Senel, Engin, Oke, Figen

Source: Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, Vol 31, Iss 3, Pp 221-227 (2023)

Subject Terms: generalized algebraic geometry codes, Code Automorphisms, Applications to coding theory and cryptography of arithmetic geometry, code automorphisms, algebraic geometry codes, Algebraic Function Fields, Generalized Algebraic Geometry Codes, geometric goppa codes, QA1-939, Algebraic Geometry Codes, primary 94b27, algebraic function fields, Algebraic functions and function fields in algebraic geometry, geometric Goppa codes, secondary 14h05, 14g50, Mathematics, Geometric Goppa Codes, Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: https://doaj.org/article/99343565b8574036bb2fa41e812a562f

Planar Convex Codes are Decidable: Planar convex codes are decidable

Authors: Boris Bukh, R. Amzi Jeffs

Source: SIAM Journal on Discrete Mathematics. 37:951-963

Subject Terms: convex, decidability, intersection patterns, Convex sets in \(2\) dimensions (including convex curves), Computational aspects related to convexity, Venn diagrams, 01 natural sciences, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), convex codes, 0101 mathematics, 52C99, 52A10, Geometric methods (including applications of algebraic geometry) applied to coding theory, realizations

File Description: application/xml

Access URL: http://arxiv.org/abs/2207.06290
https://zbmath.org/7700267
https://doi.org/10.1137/22m1511187

Codes parameterized by the edges of a bipartite graph with a perfect matching

Authors: Sarabia Manuel González, Villarreal Rafael H.

Source: Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, Vol 31, Iss 2, Pp 85-99 (2023)

Subject Terms: parameterized code, FOS: Computer and information sciences, Computer Science - Information Theory, Information Theory (cs.IT), perfect matching, Algebraic coding theory, cryptography (number-theoretic aspects), 14G50, 13P25 (Primary), 14G15, 11T71, 94B27, 94B05 (Secondary), Applications to coding theory and cryptography of arithmetic geometry, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Finite ground fields in algebraic geometry, bipartite graph, QA1-939, 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Mathematics - Combinatorics, primary 14g50, 13p25, Combinatorics (math.CO), secondary 14g15, 11t71, 94b27, 94b05, Mathematics, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Geometric methods (including applications of algebraic geometry) applied to coding theory, Linear codes (general theory)

File Description: application/xml

Access URL: http://arxiv.org/abs/2209.12846
https://zbmath.org/8036482
https://doi.org/10.2478/auom-2023-0021
https://doaj.org/article/5ec0a32c00f34b3daa6045e0015de934

Parameterized codes over graphs

Authors: Jorge Neves, Maria Vaz Pinto

Source: São Paulo Journal of Mathematical Sciences. 17:306-319

Subject Terms: FOS: Computer and information sciences, regularity, Computer Science - Information Theory, Information Theory (cs.IT), Algebraic coding theory, cryptography (number-theoretic aspects), 0102 computer and information sciences, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), 01 natural sciences, Regularity, dimension, Minimum Distance, FOS: Mathematics, minimum distance, Mathematics - Combinatorics, linear code, Combinatorics (math.CO), 0101 mathematics, Dimension, Linear Code, Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.), Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: http://arxiv.org/abs/2112.07297
https://hdl.handle.net/10316/113155

On the automorphisms of generalized algebraic geometry codes

Authors: Engin Şenel, Figen Öke

Source: Designs, Codes and Cryptography. 90:1369-1379

Subject Terms: Automorphism Groups Of Function Fields, generalized algebraic geometry codes, Code Automorphisms, Applications to coding theory and cryptography of arithmetic geometry, code automorphisms, 02 engineering and technology, Algebraic Function Fields, 01 natural sciences, automorphism groups of function fields, Automorphisms of curves, Generalized Algebraic Geometry Codes, 0202 electrical engineering, electronic engineering, information engineering, algebraic function fields, Algebraic functions and function fields in algebraic geometry, 0101 mathematics, geometric Goppa codes, Geometric Goppa Codes, Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

New constructions of abelian non-cyclic orbit codes based on parabolic subgroups and tensor products

Authors: Soleyman Askary, Nader Biranvand, Farrokh Shirjian

Source: Finite Fields and Their Applications. 103:102587

Subject Terms: Combinatorial codes, random linear network coding, subspace code, Algebraic coding theory, cryptography (number-theoretic aspects), algebraic coding theory, abelian orbit code, Geometric methods (including applications of algebraic geometry) applied to coding theory, linear groups

File Description: application/xml

A construction method of balanced rotation symmetric Boolean functions on arbitrary even number of variables with optimal algebraic immunity

Authors: Sihem Mesnager, Hui Zhang, Sihong Su

Contributors: Institut Polytechnique de Paris (IP Paris), Département Informatique et Réseaux (INFRES), Télécom ParisTech, Cybersécurité et Cryptographie (C2), Laboratoire Traitement et Communication de l'Information (LTCI), Institut Mines-Télécom Paris (IMT)-Télécom Paris, Institut Mines-Télécom Paris (IMT)-Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Institut Mines-Télécom Paris (IMT)-Télécom Paris, Institut Mines-Télécom Paris (IMT)-Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Nanjing Southeast University (SEU)

Source: Designs, Codes and Cryptography. 89:1-17

Subject Terms: Arithmetic codes, rotation symmetric Boolean function, nonlinearity, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, balancedness, algebraic immunity, Cryptography, 0202 electrical engineering, electronic engineering, information engineering, [MATH]Mathematics [math], Boolean functions, Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: https://zbmath.org/7300828
https://doi.org/10.1007/s10623-020-00806-y
https://link.springer.com/article/10.1007/s10623-020-00806-y
https://dblp.uni-trier.de/db/journals/dcc/dcc89.html#MesnagerSZ21

Accelerating smooth molecular surface calculation

Authors: Ke Yan, Ho-Lun Cheng, Zhiwei Ji, Xin Zhang, Huijuan Lu

Source: Journal of Mathematical Biology. 76:779-793

Subject Terms: Models, Molecular, 0301 basic medicine, quadratic patch, 0303 health sciences, Bézier curve, molecular modeling, Surface Properties, 4. Education, topological disk, Molecular Conformation, Physiological, cellular and medical topics, Computational Biology, Mathematical Concepts, Molecular Dynamics Simulation, Molecular Docking Simulation, Computer-aided design (modeling of curves and surfaces), 03 medical and health sciences, molecular skin surface, Numerical aspects of computer graphics, image analysis, and computational geometry, Drug Design, Computer graphics, computational geometry (digital and algorithmic aspects), Solvents, Algorithms, Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: https://pubmed.ncbi.nlm.nih.gov/28689219
https://zbmath.org/6837455
https://doi.org/10.1007/s00285-017-1156-z
https://www.ncbi.nlm.nih.gov/pubmed/28689219
https://rd.springer.com/article/10.1007/s00285-017-1156-z
https://link.springer.com/article/10.1007%2Fs00285-017-1156-z
https://link.springer.com/10.1007/s00285-017-1156-z
https://pubmed.ncbi.nlm.nih.gov/28689219/

Integral closures and weight functions over finite fields: Integral closures and weight functions over finite fields.

Authors: Ruud Pellikaan, Douglas A. Leonard

Source: Finite Fields and Their Applications. 9:479-504

Subject Terms: Towers of function fields, Algebra and Number Theory, Arithmetic theory of algebraic function fields, Applied Mathematics, Integral closure, 02 engineering and technology, Integral closure of commutative rings and ideals, 01 natural sciences, Structure theory for finite fields and commutative rings (number-theoretic aspects), AG codes, Theoretical Computer Science, Normalization, Weight function, 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Engineering(all), Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: http://www.win.tue.nl/~ruudp/paper/42.pdf
https://research.tue.nl/en/publications/81c782b0-f318-4adf-af3d-007b35103168
https://doi.org/10.1016/S1071-5797(03)00038-8
https://www.narcis.nl/publication/RecordID/oai%3Apure.tue.nl%3Apublications%2Faae4cbcd-d1f2-40eb-916c-3673eccf4488
https://ieeexplore.ieee.org/document/1023331/
https://www.win.tue.nl/~ruudp/paper/42.pdf
https://www.sciencedirect.com/science/article/abs/pii/S1071579703000388
https://www.sciencedirect.com/science/article/pii/S1071579703000388
https://www.narcis.nl/publication/RecordID/oai%3Apure.tue.nl%3Apublications%2F81c782b0-f318-4adf-af3d-007b35103168

Constructions of codes from number fields

Authors: Venkatesan Guruswami

Source: Lecture Notes in Computer Science ISBN: 9783540429111

Subject Terms: 4. Education, Algebraic coding theory, cryptography (number-theoretic aspects), 0101 mathematics, 01 natural sciences, Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: https://zbmath.org/2172540
https://doi.org/10.1109/tit.2002.808131
https://ieeexplore.ieee.org/document/1184137
https://link.springer.com/chapter/10.1007/3-540-45624-4_14
http://dblp.uni-trier.de/db/journals/tit/tit49.html#Guruswami03
https://dblp.uni-trier.de/db/journals/tit/tit49.html#Guruswami03
https://rd.springer.com/chapter/10.1007/3-540-45624-4_14
https://link.springer.com/chapter/10.1007/3-540-45624-4_14
https://dblp.uni-trier.de/db/conf/aaecc/aaecc2001.html#Guruswami01
https://core.ac.uk/display/22494284
https://rd.springer.com/chapter/10.1007/3-540-45624-4_14

A One Round Protocol for Tripartite Diffie–Hellman: A one round protocol for tripartite Diffie-Hellman

Authors: Antoine Joux

Source: Lecture Notes in Computer Science ISBN: 9783540676959

Subject Terms: pairing, cryptosystem, discrete logarithm, key exchange, Cryptography, 0202 electrical engineering, electronic engineering, information engineering, Applications to coding theory and cryptography of arithmetic geometry, 02 engineering and technology, Geometric methods (including applications of algebraic geometry) applied to coding theory, elliptic curve

File Description: application/xml

Access URL: http://cgi.di.uoa.gr/~aggelos/crypto/page4/assets/joux-tripartite.pdf
https://dblp.uni-trier.de/db/conf/ants/ants2000.html#Joux00
https://rd.springer.com/chapter/10.1007%2F10722028_23
http://portal.acm.org/citation.cfm?id=749894
https://defencemanagement.org/article/one-round-protocol-tripartite-diffie-hellman
https://procon.bg/article/one-round-protocol-tripartite-diffie-hellman

The generalized Hamming weights of some hyperelliptic codes

Authors: Mario A. de Boer

Source: Journal of Pure and Applied Algebra. 123:153-163

Subject Terms: hyperelliptic curves, Special algebraic curves and curves of low genus, Algebra and Number Theory, generalized Hamming weights, algebraic geometric codes, Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: https://research.tue.nl/en/publications/2b432d8b-abd1-477a-a2f9-f700b393ddd4
http://www.sciencedirect.com/science/article/pii/S0022404997001606
https://www.narcis.nl/publication/RecordID/oai%3Apure.tue.nl%3Apublications%2F2b432d8b-abd1-477a-a2f9-f700b393ddd4
https://www.sciencedirect.com/science/article/pii/S0022404997001606

On the Binary Codes of Steiner Triple Systems: On the binary codes of Steiner triple systems

Authors: Vladimir D. Tonchev, Alphonse Baartmans, Ivan Landjev

Source: Designs and Finite Geometries ISBN: 9781461286042

Subject Terms: hyperovals, Steiner triple system, Steiner systems in finite geometry, Triple systems, 4. Education, Blocking sets, ovals, \(k\)-arcs, ovals, 0102 computer and information sciences, 0101 mathematics, binary code, 01 natural sciences, Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: https://zbmath.org/994653
https://doi.org/10.1007/bf00130567
https://dblp.uni-trier.de/db/journals/dcc/dcc8.html#BaartmansLT96
https://digitalcommons.mtu.edu/math-fp/155/
https://rd.springer.com/chapter/10.1007/978-1-4613-1395-3_3
https://dl.acm.org/citation.cfm?id=229800
https://dl.acm.org/doi/10.1007/BF00130567
https://link.springer.com/content/pdf/10.1023/A:1018068422276.pdf

A New Approach to the Main Conjecture on Algebraic-Geometric MDS Codes: A new approach to the main conjecture on algebraic-geometric MDS codes

Authors: Judy L. Walker

Source: Codes, Designs and Geometry ISBN: 9781461286189

Subject Terms: algebraic-geometric codes, elliptic curves, MDS codes, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, Geometric methods (including applications of algebraic geometry) applied to coding theory

File Description: application/xml

Access URL: https://rd.springer.com/chapter/10.1007/978-1-4613-1423-3_11
https://link.springer.com/article/10.1023/A:1027358511882
https://link.springer.com/content/pdf/10.1023%2FA%3A1027358511882.pdf
https://dblp.uni-trier.de/db/journals/dcc/dcc9.html#Walker96

Combinatorial designs and codes over some prime fields

Authors: Stelios Georgiou, Christos Koukouvinos

Source: Journal of Statistical Planning and Inference. 135:93-106

Subject Terms: generalized orthogonal designs, construction, Combinatorial codes, self-dual codes, Diophantine equations, orthogonal designs, 0202 electrical engineering, electronic engineering, information engineering, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Geometric methods (including applications of algebraic geometry) applied to coding theory, Linear codes (general theory), Combinatorial aspects of matrices (incidence, Hadamard, etc.)

File Description: application/xml

Access URL: https://zbmath.org/2213148
https://doi.org/10.1016/j.jspi.2005.02.008
https://core.ac.uk/display/38442207
https://www.sciencedirect.com/science/article/pii/S0378375805000571
http://www.sciencedirect.com/science/article/pii/S0378375805000571

Asymptotically Good Codes from Generalized Algebraic-Geometry Codes: Asymptotically good codes from generalized algebraic-geometry codes

Authors: SPERA, Antonino Giorgio

Source: Designs, Codes and Cryptography. 37:305-312

Subject Terms: places, Special algebraic curves and curves of low genus, 0202 electrical engineering, electronic engineering, information engineering, Applications to coding theory and cryptography of arithmetic geometry, algebraic function fields, 02 engineering and technology, finite fields, 0101 mathematics, geometric Goppa codes, 01 natural sciences, Geometric methods (including applications of algebraic geometry) applied to coding theory, generalized algebraic-geometry codes

File Description: application/xml

Access URL: https://zbmath.org/2224835
https://doi.org/10.1007/s10623-004-3993-1
https://dblp.uni-trier.de/db/journals/dcc/dcc37.html#Spera05
https://core.ac.uk/display/53236834
https://link.springer.com/article/10.1007/s10623-004-3993-1
https://doi.org/10.1007/s10623-004-3993-1
https://hdl.handle.net/10447/20229