Výsledky vyhledávání - Geometric methods (including applications of algebraic geometry) applied to coding theory

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

Autoři: Giuseppe Filippone

Zdroj: Cryptography and Communications. 17:307-309

Témata: 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

Popis souboru: application/xml

On the automorphisms of generalized algebraic geometry codes

Autoři: Engin Şenel Figen Öke

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

Témata: 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

Popis souboru: application/xml

Two-character sets, Veronese varieties and Grassmannian of lines

Autoři: Cossidente A. Marino G.

Zdroj: Ricerche di Matematica. 74:207-218

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: https://hdl.handle.net/11588/959324

There are no good infinite families of toric codes

Autoři: Jason P. Bell Sean Monahan Matthew Satriano a další

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

Autoři: Senel, Engin Oke, Figen

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: https://doaj.org/article/99343565b8574036bb2fa41e812a562f

The minimum distance of a parameterized code over an even cycle

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

Zdroj: Finite Fields and Their Applications. 106:102630

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/abs/2403.05445

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

Autoři: Sihem Mesnager Hui Zhang Sihong Su a další

Přispěvatelé: Sihem Mesnager Hui Zhang Sihong Su a další

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

Témata: 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

Popis souboru: application/xml

Přístupová URL adresa: 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

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

Autoři: Sarabia Manuel González Villarreal Rafael H.

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

Témata: 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)

Popis souboru: application/xml

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

Planar Convex Codes are Decidable: Planar convex codes are decidable

Autoři: Boris Bukh R. Amzi Jeffs

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

Témata: 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

Popis souboru: application/xml

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

Parameterized codes over graphs

Autoři: Jorge Neves Maria Vaz Pinto

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

Témata: 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

Popis souboru: application/xml

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

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

Autoři: Soleyman Askary Nader Biranvand Farrokh Shirjian

Zdroj: Finite Fields and Their Applications. 103:102587

Témata: 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

Popis souboru: application/xml

Riemann–Roch spaces of the Hermitian function field with applications to algebraic geometry codes and low-discrepancy sequences: Riemann-Roch spaces of the Hermitian function field with applications to algebraic geometry codes and low-discrepancy sequences

Autoři: Gottlieb Pirsic Gretchen L. Matthews Hiren Maharaj

Zdroj: Journal of Pure and Applied Algebra. 195:261-280

Témata: divisors, Algebra and Number Theory, Well-distributed sequences and other variations, Applications to coding theory and cryptography of arithmetic geometry, 0102 computer and information sciences, Algebraic functions and function fields in algebraic geometry, 0101 mathematics, floor of a divisor, 01 natural sciences, Geometric methods (including applications of algebraic geometry) applied to coding theory

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/2136956
https://doi.org/10.1016/j.jpaa.2004.06.010
https://www.sciencedirect.com/science/article/pii/S0022404904001306
http://www.ces.clemson.edu/~gmatthe/LBasesRevision.pdf
http://www.sciencedirect.com/science/article/pii/S0022404904001306
https://core.ac.uk/display/82508601
https://dialnet.unirioja.es/servlet/articulo?codigo=1062110

Efficient root-finding algorithm with application to list decoding of algebraic-geometric codes

Autoři: Paul H. Siegel Xin-Wen Wu

Zdroj: IEEE Transactions on Information Theory. 47:2579-2587

Témata: Communications Technologies, Artificial Intelligence and Image Processing, Decoding, 05 social sciences, Applications to coding theory and cryptography of arithmetic geometry, Coding and Information Theory, root-finding algorithm, 02 engineering and technology, function fields, 0508 media and communications, algebraic-geometric codes, 0202 electrical engineering, electronic engineering, information engineering, Numerical computation of solutions to single equations, Electrical and Electronic Engineering, list decoding, Geometric methods (including applications of algebraic geometry) applied to coding theory

Popis souboru: application/xml; application/pdf

Přístupová URL adresa: https://research-repository.griffith.edu.au/bitstream/10072/55895/1/72705_1.pdf
https://ieeexplore.ieee.org/document/945273/
http://www.site.uottawa.ca/~zhcheng/efficient_root.pdf
https://core.ac.uk/display/21874315
https://research-repository.griffith.edu.au/handle/10072/55895
http://dblp.uni-trier.de/db/journals/tit/tit47.html#WuS01
https://dblp.uni-trier.de/db/journals/tit/tit47.html#WuS01

Improved decoding of Reed-Solomon and algebraic-geometric codes: Improved decoding of Reed-Solomon and algebraic-geometry codes

Autoři: Madhu Sudan Venkatesan Guruswami

Zdroj: Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280). :28-37

Témata: Reed-Solomon codes, weighted curve-fitting problem, Decoding, 4. Education, 0102 computer and information sciences, 02 engineering and technology, 16. Peace & justice, 7. Clean energy, 01 natural sciences, error-correcting code, polynomial time algorithms, algebraic-geometry codes, 0202 electrical engineering, electronic engineering, information engineering, list decoding algorithm, Geometric methods (including applications of algebraic geometry) applied to coding theory, Linear codes (general theory)

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/1503188
https://doi.org/10.1109/18.782097
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=743426
http://madhu.seas.harvard.edu/papers/1998/venkat-conf.pdf
https://madhu.seas.harvard.edu/papers/1998/venkat-conf.pdf
https://ieeexplore.ieee.org/document/743426/
https://dl.acm.org/citation.cfm?id=796393
http://ieeexplore.ieee.org/document/743426/

Generalized Bezout's theorem and its applications in coding theory: Generalized Bézout's theorem and its applications in coding theory

Autoři: Gui-Liang Feng G.A. Berg T.R.N. Rao a další

Zdroj: IEEE Transactions on Information Theory. 43:1799-1810

Témata: algebraic-geometric codes, Bézout's theorem, 0202 electrical engineering, electronic engineering, information engineering, minimum distance, generalized Hamming weights, 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, linear codes, Geometric methods (including applications of algebraic geometry) applied to coding theory, Linear codes (general theory)

Popis souboru: application/xml

Přístupová URL adresa: https://ieeexplore.ieee.org/document/641546/
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19960041298.pdf
http://ieeexplore.ieee.org/xpl/abstractKeywords.jsp?arnumber=641546
http://hdl.handle.net/2060/19960041298
https://ntrs.nasa.gov/api/citations/19960041298/downloads/19960041298.pdf
https://repository.exst.jaxa.jp/dspace/handle/a-is/103559

Algebraic-geometric codes and multidimensional cyclic codes: a unified theory and algorithms for decoding using Grobner bases: Algebraic-geometric codes and multidimensional cyclic codes: A unified theory and algorithms for decoding using Gröbner bases

Autoři: C. Heegard K. Saints

Zdroj: IEEE Transactions on Information Theory. 41:1733-1751

Témata: error-and-erasure decoding of cyclic codes, generalization of geometric BCH codes, Decoding, error-and-erasure decoding of AG codes, 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, one-point codes

Popis souboru: application/xml

Přístupová URL adresa: https://zbmath.org/884865
https://doi.org/10.1109/18.476246

An improved Bombieri-Weil bound and applications to coding theory

Autoři: Carlos J. Moreno Oscar Moreno

Zdroj: Journal of Number Theory. 42:32-46

Témata: algebraic curve, Algebra and Number Theory, number of rational points, Goppa code, Algebraic coding theory, cryptography (number-theoretic aspects), 02 engineering and technology, 01 natural sciences, error correcting BCH code, 0202 electrical engineering, electronic engineering, information engineering, Bombieri-Weil bound, minimum distance, Exponential sums, Artin-Schreier covering, dual code, 0101 mathematics, exponential sums, Geometric methods (including applications of algebraic geometry) applied to coding theory

Popis souboru: application/xml

Přístupová URL adresa: http://www.sciencedirect.com/science/article/pii/0022314X9290106Y
https://www.sciencedirect.com/science/article/pii/0022314X9290106Y

ON THE FENG-RAO BOUND FOR THE MINIMUM DISTANCE OF CERTAIN ALGEBRAIC GEOMETRY CODES: On the Feng-Rao bound for the minimum distance of certain algebraic geometry codes

Autoři: Tsuyoshi Uehara Hyeong-Kee Song

Zdroj: Kyushu Journal of Mathematics. 56:405-418

Témata: Bounds on codes, Feng-Rao bound, algebraic-geometric codes, 0202 electrical engineering, electronic engineering, information engineering, minimum distance, Applications to coding theory and cryptography of arithmetic geometry, 02 engineering and technology, 0101 mathematics, 01 natural sciences, Geometric methods (including applications of algebraic geometry) applied to coding theory

Popis souboru: application/xml

Přístupová URL adresa: https://www.jstage.jst.go.jp/article/kyushujm/56/2/56_2_405/_pdf
https://zbmath.org/1868136
https://doi.org/10.2206/kyushujm.56.405
https://www.jstage.jst.go.jp/article/kyushujm/56/2/56_2_405/_article
https://core.ac.uk/display/37845227
https://ci.nii.ac.jp/naid/130000062989

A goppa-like bound on the trellis state complexity of algebraic-geometric codes: A Goppa-like bound on the trellis state complexity of algebraic-geometric codes

Autoři: Carlos Munuera Fernando Torres

Zdroj: IEEE Transactions on Information Theory. 49:733-737

Témata: FOS: Computer and information sciences, Computer Science - Information Theory, Information Theory (cs.IT), 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Bounds on codes, Mathematics - Algebraic Geometry, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, 94B05, 94B27, 14G50, Algebraic Geometry (math.AG), Combined modulation schemes (including trellis codes) in coding theory, Geometric methods (including applications of algebraic geometry) applied to coding theory

Popis souboru: application/xml

Přístupová URL adresa: http://arxiv.org/pdf/math/0212038
http://arxiv.org/abs/math/0212038
https://zbmath.org/2172553
https://doi.org/10.1109/tit.2002.808129

A Hensel lifting to replace factorization in list-decoding of algebraic-geometric and Reed-Solomon codes

Autoři: Augot, Daniel Pecquet, Lancelot

Přispěvatelé: Augot, Daniel Pecquet, Lancelot

Zdroj: IEEE Transactions on Information Theory. 46:2605-2614

Témata: [MATH.MATH-IT] Mathematics [math]/Information Theory [math.IT], list-decoding, Reed-Solomon codes, Decoding, 0202 electrical engineering, electronic engineering, information engineering, Algebraic coding theory, cryptography (number-theoretic aspects), [INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT], algebraic geometry codes, 0102 computer and information sciences, 02 engineering and technology, Cyclic codes, 01 natural sciences, Geometric methods (including applications of algebraic geometry) applied to coding theory

Popis souboru: application/xml; application/pdf

Přístupová URL adresa: https://hal.inria.fr/inria-00509339/file/FinalSub.pdf
https://zbmath.org/1578581
https://doi.org/10.1109/18.887868
https://inria.hal.science/inria-00509339v1
https://inria.hal.science/inria-00509339v1/document
https://doi.org/10.1109/18.887868
https://dblp.uni-trier.de/db/journals/tit/tit46.html#AugotP00
https://hal.inria.fr/inria-00509339/document
https://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=19190&arnumber=887868
https://hal.inria.fr/inria-00509339
https://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=887868
http://www.lix.polytechnique.fr/~augot/IEEE_2000.pdf