- Previous Article
- AMC Home
- This Issue
-
Next Article
Variation on correlation immune Boolean and vectorial functions
On the duality and the direction of polycyclic codes
1. | Math Dept., King Abdulaziz University, Jeddah, Saudi Arabia |
2. | University of Scranton, Scranton, PA 18518, United States |
3. | University of Artois, Faculté J. Perrin, 62300 Lens, France |
4. | CNRS/LAGA, University of Paris 8, 93 526 Saint-Denis, France |
References:
[1] |
K. Betsumiya and M. Harada, Binary optimal odd formally self-dual codes, Des. Codes Crypt., 23 (2001), 11-22.
doi: 10.1023/A:1011203416769. |
[2] |
J. Fields, P. Gaborit, V. Pless and W. C. Huffman, On the classification of extremal even formally self-dual codes of lengths $20$ and $22$, Discrete Appl. Math., 111 (2001), 75-86.
doi: 10.1016/S0166-218X(00)00345-0. |
[3] |
M. Grassl, Bounds on the minimum distance of linear codes,, available online at , ().
|
[4] |
W. C. Huffman and V. Pless, Fundamentals of Error Correcting Codes, Cambridge Univ. Press, 2003.
doi: 10.1017/CBO9780511807077. |
[5] |
T. Kasami, Optimum shortened cyclic codes for burst-error correction, IEEE Trans. Inform. Theory, 9 (1963), 105-109. |
[6] |
J.-L. Kim and V. Pless, A note on formally self-dual even codes of length divisible by 8, Finite Fields Appl., 13 (2007), 224-229.
doi: 10.1016/j.ffa.2005.09.006. |
[7] |
S. R. Lopez-Permouth, B. R. Parra-Avila and S. Szabo, Dual generalizations of the concept of cyclicity of codes, Adv. Math. Commun., 3 (2009), 227-234.
doi: 10.3934/amc.2009.3.227. |
[8] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977. |
[9] |
M. Matsuoka, $\theta$-polycyclic codes and $\theta$-sequential codes over finite fields, Int. J. Algebra, 5 (2011), 65-70. |
[10] |
W. W. Peterson and E. J. Weldon, Error Correcting Codes, MIT Press, 1972. |
[11] |
E. M. Rains and N. J. A. Sloane, Self-dual codes, in Handbook of Coding Theory, Elsevier, Amsterdam, 1998. |
[12] |
J. Wood, Duality for modules over finite rings and applications to coding theory, Amer. J. Math., 121 (1999), 555-575. |
show all references
References:
[1] |
K. Betsumiya and M. Harada, Binary optimal odd formally self-dual codes, Des. Codes Crypt., 23 (2001), 11-22.
doi: 10.1023/A:1011203416769. |
[2] |
J. Fields, P. Gaborit, V. Pless and W. C. Huffman, On the classification of extremal even formally self-dual codes of lengths $20$ and $22$, Discrete Appl. Math., 111 (2001), 75-86.
doi: 10.1016/S0166-218X(00)00345-0. |
[3] |
M. Grassl, Bounds on the minimum distance of linear codes,, available online at , ().
|
[4] |
W. C. Huffman and V. Pless, Fundamentals of Error Correcting Codes, Cambridge Univ. Press, 2003.
doi: 10.1017/CBO9780511807077. |
[5] |
T. Kasami, Optimum shortened cyclic codes for burst-error correction, IEEE Trans. Inform. Theory, 9 (1963), 105-109. |
[6] |
J.-L. Kim and V. Pless, A note on formally self-dual even codes of length divisible by 8, Finite Fields Appl., 13 (2007), 224-229.
doi: 10.1016/j.ffa.2005.09.006. |
[7] |
S. R. Lopez-Permouth, B. R. Parra-Avila and S. Szabo, Dual generalizations of the concept of cyclicity of codes, Adv. Math. Commun., 3 (2009), 227-234.
doi: 10.3934/amc.2009.3.227. |
[8] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977. |
[9] |
M. Matsuoka, $\theta$-polycyclic codes and $\theta$-sequential codes over finite fields, Int. J. Algebra, 5 (2011), 65-70. |
[10] |
W. W. Peterson and E. J. Weldon, Error Correcting Codes, MIT Press, 1972. |
[11] |
E. M. Rains and N. J. A. Sloane, Self-dual codes, in Handbook of Coding Theory, Elsevier, Amsterdam, 1998. |
[12] |
J. Wood, Duality for modules over finite rings and applications to coding theory, Amer. J. Math., 121 (1999), 555-575. |
[1] |
Stefka Bouyuklieva, Iliya Bouyukliev. Classification of the extremal formally self-dual even codes of length 30. Advances in Mathematics of Communications, 2010, 4 (3) : 433-439. doi: 10.3934/amc.2010.4.433 |
[2] |
Masaaki Harada, Katsushi Waki. New extremal formally self-dual even codes of length 30. Advances in Mathematics of Communications, 2009, 3 (4) : 311-316. doi: 10.3934/amc.2009.3.311 |
[3] |
Steven T. Dougherty, Joe Gildea, Abidin Kaya, Bahattin Yildiz. New self-dual and formally self-dual codes from group ring constructions. Advances in Mathematics of Communications, 2020, 14 (1) : 11-22. doi: 10.3934/amc.2020002 |
[4] |
Gabriele Nebe, Wolfgang Willems. On self-dual MRD codes. Advances in Mathematics of Communications, 2016, 10 (3) : 633-642. doi: 10.3934/amc.2016031 |
[5] |
Somphong Jitman, San Ling, Ekkasit Sangwisut. On self-dual cyclic codes of length $p^a$ over $GR(p^2,s)$. Advances in Mathematics of Communications, 2016, 10 (2) : 255-273. doi: 10.3934/amc.2016004 |
[6] |
Masaaki Harada, Akihiro Munemasa. Classification of self-dual codes of length 36. Advances in Mathematics of Communications, 2012, 6 (2) : 229-235. doi: 10.3934/amc.2012.6.229 |
[7] |
Stefka Bouyuklieva, Anton Malevich, Wolfgang Willems. On the performance of binary extremal self-dual codes. Advances in Mathematics of Communications, 2011, 5 (2) : 267-274. doi: 10.3934/amc.2011.5.267 |
[8] |
Nikolay Yankov, Damyan Anev, Müberra Gürel. Self-dual codes with an automorphism of order 13. Advances in Mathematics of Communications, 2017, 11 (3) : 635-645. doi: 10.3934/amc.2017047 |
[9] |
Steven T. Dougherty, Cristina Fernández-Córdoba, Roger Ten-Valls, Bahattin Yildiz. Quaternary group ring codes: Ranks, kernels and self-dual codes. Advances in Mathematics of Communications, 2020, 14 (2) : 319-332. doi: 10.3934/amc.2020023 |
[10] |
Keita Ishizuka, Ken Saito. Construction for both self-dual codes and LCD codes. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2021070 |
[11] |
Masaaki Harada, Akihiro Munemasa. On the covering radii of extremal doubly even self-dual codes. Advances in Mathematics of Communications, 2007, 1 (2) : 251-256. doi: 10.3934/amc.2007.1.251 |
[12] |
Hyun Jin Kim, Heisook Lee, June Bok Lee, Yoonjin Lee. Construction of self-dual codes with an automorphism of order $p$. Advances in Mathematics of Communications, 2011, 5 (1) : 23-36. doi: 10.3934/amc.2011.5.23 |
[13] |
Minjia Shi, Daitao Huang, Lin Sok, Patrick Solé. Double circulant self-dual and LCD codes over Galois rings. Advances in Mathematics of Communications, 2019, 13 (1) : 171-183. doi: 10.3934/amc.2019011 |
[14] |
Bram van Asch, Frans Martens. Lee weight enumerators of self-dual codes and theta functions. Advances in Mathematics of Communications, 2008, 2 (4) : 393-402. doi: 10.3934/amc.2008.2.393 |
[15] |
Bram van Asch, Frans Martens. A note on the minimum Lee distance of certain self-dual modular codes. Advances in Mathematics of Communications, 2012, 6 (1) : 65-68. doi: 10.3934/amc.2012.6.65 |
[16] |
Katherine Morrison. An enumeration of the equivalence classes of self-dual matrix codes. Advances in Mathematics of Communications, 2015, 9 (4) : 415-436. doi: 10.3934/amc.2015.9.415 |
[17] |
Steven T. Dougherty, Joe Gildea, Adrian Korban, Abidin Kaya. Composite constructions of self-dual codes from group rings and new extremal self-dual binary codes of length 68. Advances in Mathematics of Communications, 2020, 14 (4) : 677-702. doi: 10.3934/amc.2020037 |
[18] |
Suat Karadeniz, Bahattin Yildiz. New extremal binary self-dual codes of length $68$ from $R_2$-lifts of binary self-dual codes. Advances in Mathematics of Communications, 2013, 7 (2) : 219-229. doi: 10.3934/amc.2013.7.219 |
[19] |
Steven T. Dougherty, Cristina Fernández-Córdoba. Codes over $\mathbb{Z}_{2^k}$, Gray map and self-dual codes. Advances in Mathematics of Communications, 2011, 5 (4) : 571-588. doi: 10.3934/amc.2011.5.571 |
[20] |
Masaaki Harada. Note on the residue codes of self-dual $\mathbb{Z}_4$-codes having large minimum Lee weights. Advances in Mathematics of Communications, 2016, 10 (4) : 695-706. doi: 10.3934/amc.2016035 |
2020 Impact Factor: 0.935
Tools
Metrics
Other articles
by authors
[Back to Top]