
-
Previous Article
Completely regular codes by concatenating Hamming codes
- AMC Home
- This Issue
-
Next Article
Several infinite families of p-ary weakly regular bent functions
Locally recoverable codes with availability t≥2 from fiber products of curves
1. | Department of Mathematics and Statistics, Villanova University, Villanova, PA 19085, USA |
2. | Department of Mathematics and Computer Science, Colorado College, Colorado Springs, CO 80903, USA |
3. | Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, USA |
We generalize the construction of locally recoverable codes on algebraic curves given by Barg, Tamo and Vlăduţ [
References:
[1] |
M. Abdón, J. Bezerra and L. Quoos,
Further examples of maximal curves, Journal of Pure and Applied Algebra, 213 (2009), 1192-1196.
doi: 10.1016/j.jpaa.2008.11.037. |
[2] |
E. Ballico and A. Ravagnani,
Embedding Suzuki curves in $\Bbb P^4$, Journal of Commutative Algebra, 7 (2015), 149-166.
doi: 10.1216/JCA-2015-7-2-149. |
[3] |
A. Barg, K. Haymaker, E. W. Howe, G. L. Matthews and A. Várilly-Alvarado, Locally recoverable codes from algebraic curves and surfaces, Algebraic Geometry for Coding Theory and
Cryptography, (2017), 95–127, arXiv: 1701.05212.
doi: 10.1007/978-3-319-63931-4_4. |
[4] |
A. Barg, I. Tamo and S. Vlădut¸, Locally recoverable codes on algebraic curves, Proceedings of the IEEE Int. Symp. Info. Theory, (2015), 1252–1256, Extended version: arXiv: 1603.08876.
doi: 10.1109/ISIT.2015.7282656. |
[5] |
A. Eid and I. Duursma, Smooth embeddings for the Suzuki and Ree curves, Proceedings of the conference on Arithmetic, Geometry and Coding Theory (AGCT 2013), Contemporary Mathematics Series (AMS), 637 (2015), 251–291. |
[6] |
A. Garcia, C. Güneri and H. Stichtenoth,
A generalization of the Giulietti-Korchmáros maximal curve, Advances in Geometry, 10 (2010), 427-434.
|
[7] |
M. Giulietti and G. Korchmáros,
A new family of maximal curves over a finite field, Math. Ann., 343 (2009), 229-245.
doi: 10.1007/s00208-008-0270-z. |
[8] |
M. Giulietti, G. Korchmáros and F. Torres,
Quotient curves of the Suzuki curve, Acta Arithmetica, 122 (2006), 245-274.
doi: 10.4064/aa122-3-3. |
[9] |
R. Guralnick, B. Malmskog and R. Pries,
The automorphism groups of a family of maximal curves, Journal of Algebra, 361 (2012), 92-106.
doi: 10.1016/j.jalgebra.2012.03.036. |
[10] |
J. Hansen, Deligne-Lusztig varieties and group codes, in Coding Theory and Algebraic Geometry, Lecture Notes in Mathematics, 1518 (1992), 63–81. |
[11] |
Q. Liu, Algebraic Geometry and Arithmetic Curves, Oxford Graduate Texts in Mathematics, 2002. |
[12] |
H.-G. Rück and H. Stichtenoth,
A characterization of Hermitian function fields over finite fields, J. Reine Angew. Math., 457 (1994), 185-188.
|
[13] |
H. Stichtenoth, Algebraic Function Fields and Codes, Springer-Verlag, Berlin, 2009. |
[14] |
G. van der Geer and M. van der Vlugt, How to construct curves over finite fields with many points, in Arithmetic Geometry (Cortona, 1994), Symposia Mathematica Cambridge: Cambridge University Press, 37 (1997), 169–189. |
show all references
References:
[1] |
M. Abdón, J. Bezerra and L. Quoos,
Further examples of maximal curves, Journal of Pure and Applied Algebra, 213 (2009), 1192-1196.
doi: 10.1016/j.jpaa.2008.11.037. |
[2] |
E. Ballico and A. Ravagnani,
Embedding Suzuki curves in $\Bbb P^4$, Journal of Commutative Algebra, 7 (2015), 149-166.
doi: 10.1216/JCA-2015-7-2-149. |
[3] |
A. Barg, K. Haymaker, E. W. Howe, G. L. Matthews and A. Várilly-Alvarado, Locally recoverable codes from algebraic curves and surfaces, Algebraic Geometry for Coding Theory and
Cryptography, (2017), 95–127, arXiv: 1701.05212.
doi: 10.1007/978-3-319-63931-4_4. |
[4] |
A. Barg, I. Tamo and S. Vlădut¸, Locally recoverable codes on algebraic curves, Proceedings of the IEEE Int. Symp. Info. Theory, (2015), 1252–1256, Extended version: arXiv: 1603.08876.
doi: 10.1109/ISIT.2015.7282656. |
[5] |
A. Eid and I. Duursma, Smooth embeddings for the Suzuki and Ree curves, Proceedings of the conference on Arithmetic, Geometry and Coding Theory (AGCT 2013), Contemporary Mathematics Series (AMS), 637 (2015), 251–291. |
[6] |
A. Garcia, C. Güneri and H. Stichtenoth,
A generalization of the Giulietti-Korchmáros maximal curve, Advances in Geometry, 10 (2010), 427-434.
|
[7] |
M. Giulietti and G. Korchmáros,
A new family of maximal curves over a finite field, Math. Ann., 343 (2009), 229-245.
doi: 10.1007/s00208-008-0270-z. |
[8] |
M. Giulietti, G. Korchmáros and F. Torres,
Quotient curves of the Suzuki curve, Acta Arithmetica, 122 (2006), 245-274.
doi: 10.4064/aa122-3-3. |
[9] |
R. Guralnick, B. Malmskog and R. Pries,
The automorphism groups of a family of maximal curves, Journal of Algebra, 361 (2012), 92-106.
doi: 10.1016/j.jalgebra.2012.03.036. |
[10] |
J. Hansen, Deligne-Lusztig varieties and group codes, in Coding Theory and Algebraic Geometry, Lecture Notes in Mathematics, 1518 (1992), 63–81. |
[11] |
Q. Liu, Algebraic Geometry and Arithmetic Curves, Oxford Graduate Texts in Mathematics, 2002. |
[12] |
H.-G. Rück and H. Stichtenoth,
A characterization of Hermitian function fields over finite fields, J. Reine Angew. Math., 457 (1994), 185-188.
|
[13] |
H. Stichtenoth, Algebraic Function Fields and Codes, Springer-Verlag, Berlin, 2009. |
[14] |
G. van der Geer and M. van der Vlugt, How to construct curves over finite fields with many points, in Arithmetic Geometry (Cortona, 1994), Symposia Mathematica Cambridge: Cambridge University Press, 37 (1997), 169–189. |





270 | 3252 | 215 |
260 | 3132 | 425 |
250 | 3012 | 635 |
240 | 2892 | 845 |
230 | 2772 | 1055 |
220 | 2652 | 1265 |
210 | 2532 | 1475 |
270 | 3252 | 215 |
260 | 3132 | 425 |
250 | 3012 | 635 |
240 | 2892 | 845 |
230 | 2772 | 1055 |
220 | 2652 | 1265 |
210 | 2532 | 1475 |
[1] |
Valentina Casarino, Paolo Ciatti, Silvia Secco. Product structures and fractional integration along curves in the space. Discrete and Continuous Dynamical Systems - S, 2013, 6 (3) : 619-635. doi: 10.3934/dcdss.2013.6.619 |
[2] |
Joseph H. Silverman. Local-global aspects of (hyper)elliptic curves over (in)finite fields. Advances in Mathematics of Communications, 2010, 4 (2) : 101-114. doi: 10.3934/amc.2010.4.101 |
[3] |
Eric Todd Quinto, Hans Rullgård. Local singularity reconstruction from integrals over curves in $\mathbb{R}^3$. Inverse Problems and Imaging, 2013, 7 (2) : 585-609. doi: 10.3934/ipi.2013.7.585 |
[4] |
Stefano Marò. Relativistic pendulum and invariant curves. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 1139-1162. doi: 10.3934/dcds.2015.35.1139 |
[5] |
Gian-Italo Bischi, Laura Gardini, Fabio Tramontana. Bifurcation curves in discontinuous maps. Discrete and Continuous Dynamical Systems - B, 2010, 13 (2) : 249-267. doi: 10.3934/dcdsb.2010.13.249 |
[6] |
Carlos Munuera, Alonso Sepúlveda, Fernando Torres. Castle curves and codes. Advances in Mathematics of Communications, 2009, 3 (4) : 399-408. doi: 10.3934/amc.2009.3.399 |
[7] |
Vladimir Georgiev, Eugene Stepanov. Metric cycles, curves and solenoids. Discrete and Continuous Dynamical Systems, 2014, 34 (4) : 1443-1463. doi: 10.3934/dcds.2014.34.1443 |
[8] |
Martin Möller. Shimura and Teichmüller curves. Journal of Modern Dynamics, 2011, 5 (1) : 1-32. doi: 10.3934/jmd.2011.5.1 |
[9] |
Lawrence Ein, Wenbo Niu, Jinhyung Park. On blowup of secant varieties of curves. Electronic Research Archive, 2021, 29 (6) : 3649-3654. doi: 10.3934/era.2021055 |
[10] |
Philip N. J. Eagle, Steven D. Galbraith, John B. Ong. Point compression for Koblitz elliptic curves. Advances in Mathematics of Communications, 2011, 5 (1) : 1-10. doi: 10.3934/amc.2011.5.1 |
[11] |
Adrian Tudorascu. On absolutely continuous curves of probabilities on the line. Discrete and Continuous Dynamical Systems, 2019, 39 (9) : 5105-5124. doi: 10.3934/dcds.2019207 |
[12] |
Nicholas Hoell, Guillaume Bal. Ray transforms on a conformal class of curves. Inverse Problems and Imaging, 2014, 8 (1) : 103-125. doi: 10.3934/ipi.2014.8.103 |
[13] |
M. J. Jacobson, R. Scheidler, A. Stein. Cryptographic protocols on real hyperelliptic curves. Advances in Mathematics of Communications, 2007, 1 (2) : 197-221. doi: 10.3934/amc.2007.1.197 |
[14] |
Philip Korman. Curves of equiharmonic solutions, and problems at resonance. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2847-2860. doi: 10.3934/dcds.2014.34.2847 |
[15] |
Michael Khanevsky. Non-autonomous curves on surfaces. Journal of Modern Dynamics, 2021, 17: 305-317. doi: 10.3934/jmd.2021010 |
[16] |
Nazar Arakelian, Saeed Tafazolian, Fernando Torres. On the spectrum for the genera of maximal curves over small fields. Advances in Mathematics of Communications, 2018, 12 (1) : 143-149. doi: 10.3934/amc.2018009 |
[17] |
Koichi Osaki, Hirotoshi Satoh, Shigetoshi Yazaki. Towards modelling spiral motion of open plane curves. Discrete and Continuous Dynamical Systems - S, 2015, 8 (5) : 1009-1022. doi: 10.3934/dcdss.2015.8.1009 |
[18] |
Stefania Fanali, Massimo Giulietti, Irene Platoni. On maximal curves over finite fields of small order. Advances in Mathematics of Communications, 2012, 6 (1) : 107-120. doi: 10.3934/amc.2012.6.107 |
[19] |
Knut Hüper, Irina Markina, Fátima Silva Leite. A Lagrangian approach to extremal curves on Stiefel manifolds. Journal of Geometric Mechanics, 2021, 13 (1) : 55-72. doi: 10.3934/jgm.2020031 |
[20] |
Chuangqiang Hu, Shudi Yang. Multi-point codes from the GGS curves. Advances in Mathematics of Communications, 2020, 14 (2) : 279-299. doi: 10.3934/amc.2020020 |
2021 Impact Factor: 1.015
Tools
Metrics
Other articles
by authors
[Back to Top]