-
Previous Article
An approach to the performance of SPC product codes on the erasure channel
- AMC Home
- This Issue
-
Next Article
Editorial
New examples of non-abelian group codes
1. | Department of Mathematics, University of Oviedo, Calvo Sotelo, s/n, 33007 Oviedo, Spain, Spain |
2. | Department of Mechanics and Mathematics, Moscow State University, Russian Federation, Russian Federation |
3. | Departamento de Matemáticas, Universidad de Oviedo, C/ Calvo Sotelo s/n, 33007 Oviedo |
References:
[1] |
J. J. Bernal, Á del Río and J. J. Simón, An intrinsical description of group codes,, Des. Codes Crypt., 51 (2009), 289.
doi: 10.1007/s10623-008-9261-z. |
[2] |
E. Couselo, S. González, V. Markov and A. Nechaev, Loop codes,, Discr. Math. Appl., 14 (2004), 163.
doi: 10.1515/156939204872347. |
[3] |
R. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras,, John Wiley & Sons, (1962).
|
[4] |
C. García Pillado, S. González, V. Markov, C. Martínez and A. Nechaev, Group codes which are not abelian group codes,, in Proc. 3rd Int. Castle Meeting Coding Theory Appl. (eds. J. Borges and M. Villanueva), (2011), 123. Google Scholar |
[5] |
C. García Pillado, S. González, V. Markov, C. Martínez and A. Nechaev, When all group codes of a noncommutative group are abelian (a computational approach),, Fund. Appl. Math., 17 (2012), 75.
doi: 10.1007/s10958-012-1006-x. |
[6] |
C. García Pillado, S. González, V. Markov, C. Martínez and A. Nechaev, Group codes over non-abelian groups,, J. Algebra Appl., 12 (2013).
doi: 10.1142/S0219498813500370. |
[7] |
M. Grassl, Bounds on the minimum distance of linear codes and quantum codes,, available online at , (). Google Scholar |
[8] |
M. Khan, R. K. Sharma and J. B. Srivastava, The unit group of $FS_4$,, in Acta Math. Hungar., 118 (2008), 105.
doi: 10.1007/s10474-007-6169-4. |
[9] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes,, North Holland, (1974). Google Scholar |
[10] |
D. S. Passman, The Algebraic Structure of Group Rings,, John Wiley & Sons, (1977).
|
show all references
References:
[1] |
J. J. Bernal, Á del Río and J. J. Simón, An intrinsical description of group codes,, Des. Codes Crypt., 51 (2009), 289.
doi: 10.1007/s10623-008-9261-z. |
[2] |
E. Couselo, S. González, V. Markov and A. Nechaev, Loop codes,, Discr. Math. Appl., 14 (2004), 163.
doi: 10.1515/156939204872347. |
[3] |
R. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras,, John Wiley & Sons, (1962).
|
[4] |
C. García Pillado, S. González, V. Markov, C. Martínez and A. Nechaev, Group codes which are not abelian group codes,, in Proc. 3rd Int. Castle Meeting Coding Theory Appl. (eds. J. Borges and M. Villanueva), (2011), 123. Google Scholar |
[5] |
C. García Pillado, S. González, V. Markov, C. Martínez and A. Nechaev, When all group codes of a noncommutative group are abelian (a computational approach),, Fund. Appl. Math., 17 (2012), 75.
doi: 10.1007/s10958-012-1006-x. |
[6] |
C. García Pillado, S. González, V. Markov, C. Martínez and A. Nechaev, Group codes over non-abelian groups,, J. Algebra Appl., 12 (2013).
doi: 10.1142/S0219498813500370. |
[7] |
M. Grassl, Bounds on the minimum distance of linear codes and quantum codes,, available online at , (). Google Scholar |
[8] |
M. Khan, R. K. Sharma and J. B. Srivastava, The unit group of $FS_4$,, in Acta Math. Hungar., 118 (2008), 105.
doi: 10.1007/s10474-007-6169-4. |
[9] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes,, North Holland, (1974). Google Scholar |
[10] |
D. S. Passman, The Algebraic Structure of Group Rings,, John Wiley & Sons, (1977).
|
[1] |
Masaaki Harada, Ethan Novak, Vladimir D. Tonchev. The weight distribution of the self-dual $[128,64]$ polarity design code. Advances in Mathematics of Communications, 2016, 10 (3) : 643-648. doi: 10.3934/amc.2016032 |
[2] |
Eldho K. Thomas, Nadya Markin, Frédérique Oggier. On Abelian group representability of finite groups. Advances in Mathematics of Communications, 2014, 8 (2) : 139-152. doi: 10.3934/amc.2014.8.139 |
[3] |
Martino Borello, Francesca Dalla Volta, Gabriele Nebe. The automorphism group of a self-dual $[72,36,16]$ code does not contain $\mathcal S_3$, $\mathcal A_4$ or $D_8$. Advances in Mathematics of Communications, 2013, 7 (4) : 503-510. doi: 10.3934/amc.2013.7.503 |
[4] |
Denis S. Krotov, Patric R. J. Östergård, Olli Pottonen. Non-existence of a ternary constant weight $(16,5,15;2048)$ diameter perfect code. Advances in Mathematics of Communications, 2016, 10 (2) : 393-399. doi: 10.3934/amc.2016013 |
[5] |
Laura Luzzi, Ghaya Rekaya-Ben Othman, Jean-Claude Belfiore. Algebraic reduction for the Golden Code. Advances in Mathematics of Communications, 2012, 6 (1) : 1-26. doi: 10.3934/amc.2012.6.1 |
[6] |
Irene Márquez-Corbella, Edgar Martínez-Moro, Emilio Suárez-Canedo. On the ideal associated to a linear code. Advances in Mathematics of Communications, 2016, 10 (2) : 229-254. doi: 10.3934/amc.2016003 |
[7] |
Serhii Dyshko. On extendability of additive code isometries. Advances in Mathematics of Communications, 2016, 10 (1) : 45-52. doi: 10.3934/amc.2016.10.45 |
[8] |
John Franks, Michael Handel. Some virtually abelian subgroups of the group of analytic symplectic diffeomorphisms of a surface. Journal of Modern Dynamics, 2013, 7 (3) : 369-394. doi: 10.3934/jmd.2013.7.369 |
[9] |
Olof Heden. The partial order of perfect codes associated to a perfect code. Advances in Mathematics of Communications, 2007, 1 (4) : 399-412. doi: 10.3934/amc.2007.1.399 |
[10] |
Selim Esedoḡlu, Fadil Santosa. Error estimates for a bar code reconstruction method. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1889-1902. doi: 10.3934/dcdsb.2012.17.1889 |
[11] |
Alexander Barg, Arya Mazumdar, Gilles Zémor. Weight distribution and decoding of codes on hypergraphs. Advances in Mathematics of Communications, 2008, 2 (4) : 433-450. doi: 10.3934/amc.2008.2.433 |
[12] |
M. Delgado Pineda, E. A. Galperin, P. Jiménez Guerra. MAPLE code of the cubic algorithm for multiobjective optimization with box constraints. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 407-424. doi: 10.3934/naco.2013.3.407 |
[13] |
Andrew Klapper, Andrew Mertz. The two covering radius of the two error correcting BCH code. Advances in Mathematics of Communications, 2009, 3 (1) : 83-95. doi: 10.3934/amc.2009.3.83 |
[14] |
Masaaki Harada, Takuji Nishimura. An extremal singly even self-dual code of length 88. Advances in Mathematics of Communications, 2007, 1 (2) : 261-267. doi: 10.3934/amc.2007.1.261 |
[15] |
José Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro. Information--bit error rate and false positives in an MDS code. Advances in Mathematics of Communications, 2015, 9 (2) : 149-168. doi: 10.3934/amc.2015.9.149 |
[16] |
Sergio Estrada, J. R. García-Rozas, Justo Peralta, E. Sánchez-García. Group convolutional codes. Advances in Mathematics of Communications, 2008, 2 (1) : 83-94. doi: 10.3934/amc.2008.2.83 |
[17] |
Heping Liu, Yu Liu. Refinable functions on the Heisenberg group. Communications on Pure & Applied Analysis, 2007, 6 (3) : 775-787. doi: 10.3934/cpaa.2007.6.775 |
[18] |
Stefan Haller, Tomasz Rybicki, Josef Teichmann. Smooth perfectness for the group of diffeomorphisms. Journal of Geometric Mechanics, 2013, 5 (3) : 281-294. doi: 10.3934/jgm.2013.5.281 |
[19] |
Daniele D'angeli, Alfredo Donno, Michel Matter, Tatiana Nagnibeda. Schreier graphs of the Basilica group. Journal of Modern Dynamics, 2010, 4 (1) : 167-205. doi: 10.3934/jmd.2010.4.167 |
[20] |
Van Cyr, John Franks, Bryna Kra, Samuel Petite. Distortion and the automorphism group of a shift. Journal of Modern Dynamics, 2018, 13: 147-161. doi: 10.3934/jmd.2018015 |
2018 Impact Factor: 0.879
Tools
Metrics
Other articles
by authors
[Back to Top]