-
Previous Article
A practicable timing attack against HQC and its countermeasure
- AMC Home
- This Issue
-
Next Article
Cryptanalysis and enhancement of multi factor remote user authentication scheme based on signcryption
Additive and linear conjucyclic codes over $ {\mathbb{F}}_4 $
1. | Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE |
2. | University of Scranton, Scranton, PA 18510, USA |
Conjucyclic codes were first introduced by Calderbank, Rains, Shor and Sloane in [
References:
[1] |
A. R. Calderbank, E. Rains, P. W. Shor and N. J. A. Sloane,
Quantum error correction via codes over ${\mathbb{F}}_{4}$, IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.
doi: 10.1109/18.681315. |
[2] |
S. T. Dougherty, Algebraic Coding Theory over Finite Commutative Rings, SpringerBriefs in Mathematics, Springer, Cham, 2017.
doi: 10.1007/978-3-319-59806-2. |
[3] |
S. T. Dougherty, J.-L. Kim and N. Lee,
Additive self-dual codes over fields of even order, Bull. Korean Math. Soc., 55 (2018), 341-357.
doi: 10.4134/BKMS.b160842. |
[4] |
S. T. Dougherty and S. Meyers, Orthogonality from Group Characters, work in progress. Google Scholar |
[5] |
T. W. Hungerford, Algebra, Graduate Texts in Mathematics, Vol. 73, Springer-Verlag, New York-Berlin, 1980. |
[6] |
J.-L. Kim and N. Lee,
Secret sharing schemes based on additive codes over ${\mathbb{F}}_{4}$, Appl. Algebra Engrg. Comm. Comput., 28 (2017), 79-97.
doi: 10.1007/s00200-016-0296-5. |
[7] |
D. Radkova and A. J. Van Zanten,
Constacyclic codes as invariant subspaces, Linear Algebra Appl., 430 (2009), 855-864.
doi: 10.1016/j.laa.2008.09.036. |
show all references
References:
[1] |
A. R. Calderbank, E. Rains, P. W. Shor and N. J. A. Sloane,
Quantum error correction via codes over ${\mathbb{F}}_{4}$, IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.
doi: 10.1109/18.681315. |
[2] |
S. T. Dougherty, Algebraic Coding Theory over Finite Commutative Rings, SpringerBriefs in Mathematics, Springer, Cham, 2017.
doi: 10.1007/978-3-319-59806-2. |
[3] |
S. T. Dougherty, J.-L. Kim and N. Lee,
Additive self-dual codes over fields of even order, Bull. Korean Math. Soc., 55 (2018), 341-357.
doi: 10.4134/BKMS.b160842. |
[4] |
S. T. Dougherty and S. Meyers, Orthogonality from Group Characters, work in progress. Google Scholar |
[5] |
T. W. Hungerford, Algebra, Graduate Texts in Mathematics, Vol. 73, Springer-Verlag, New York-Berlin, 1980. |
[6] |
J.-L. Kim and N. Lee,
Secret sharing schemes based on additive codes over ${\mathbb{F}}_{4}$, Appl. Algebra Engrg. Comm. Comput., 28 (2017), 79-97.
doi: 10.1007/s00200-016-0296-5. |
[7] |
D. Radkova and A. J. Van Zanten,
Constacyclic codes as invariant subspaces, Linear Algebra Appl., 430 (2009), 855-864.
doi: 10.1016/j.laa.2008.09.036. |
The code |
Basis |
The code |
Basis |
[1] |
Yuan Cao, Yonglin Cao, Hai Q. Dinh, Ramakrishna Bandi, Fang-Wei Fu. An explicit representation and enumeration for negacyclic codes of length $ 2^kn $ over $ \mathbb{Z}_4+u\mathbb{Z}_4 $. Advances in Mathematics of Communications, 2021, 15 (2) : 291-309. doi: 10.3934/amc.2020067 |
[2] |
Hai Q. Dinh, Bac T. Nguyen, Paravee Maneejuk. Constacyclic codes of length $ 8p^s $ over $ \mathbb F_{p^m} + u\mathbb F_{p^m} $. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020123 |
[3] |
Junchao Zhou, Yunge Xu, Lisha Wang, Nian Li. Nearly optimal codebooks from generalized Boolean bent functions over $ \mathbb{Z}_{4} $. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020121 |
[4] |
Saadoun Mahmoudi, Karim Samei. Codes over $ \frak m $-adic completion rings. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020122 |
[5] |
Manuel del Pino, Monica Musso, Juncheng Wei, Yifu Zhou. Type Ⅱ finite time blow-up for the energy critical heat equation in $ \mathbb{R}^4 $. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3327-3355. doi: 10.3934/dcds.2020052 |
[6] |
Luca Battaglia, Francesca Gladiali, Massimo Grossi. Asymptotic behavior of minimal solutions of $ -\Delta u = \lambda f(u) $ as $ \lambda\to-\infty $. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 681-700. doi: 10.3934/dcds.2020293 |
[7] |
Guoyuan Chen, Yong Liu, Juncheng Wei. Nondegeneracy of harmonic maps from $ {{\mathbb{R}}^{2}} $ to $ {{\mathbb{S}}^{2}} $. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3215-3233. doi: 10.3934/dcds.2019228 |
[8] |
Mathew Gluck. Classification of solutions to a system of $ n^{\rm th} $ order equations on $ \mathbb R^n $. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5413-5436. doi: 10.3934/cpaa.2020246 |
[9] |
Hongwei Liu, Jingge Liu. On $ \sigma $-self-orthogonal constacyclic codes over $ \mathbb F_{p^m}+u\mathbb F_{p^m} $. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020127 |
[10] |
Denis Bonheure, Silvia Cingolani, Simone Secchi. Concentration phenomena for the Schrödinger-Poisson system in $ \mathbb{R}^2 $. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020447 |
[11] |
Michal Fečkan, Kui Liu, JinRong Wang. $ (\omega,\mathbb{T}) $-periodic solutions of impulsive evolution equations. Evolution Equations & Control Theory, 2021 doi: 10.3934/eect.2021006 |
[12] |
Lei Liu, Li Wu. Multiplicity of closed characteristics on $ P $-symmetric compact convex hypersurfaces in $ \mathbb{R}^{2n} $. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020378 |
[13] |
Wenqiang Zhao, Yijin Zhang. High-order Wong-Zakai approximations for non-autonomous stochastic $ p $-Laplacian equations on $ \mathbb{R}^N $. Communications on Pure & Applied Analysis, 2021, 20 (1) : 243-280. doi: 10.3934/cpaa.2020265 |
[14] |
Hongming Ru, Chunming Tang, Yanfeng Qi, Yuxiao Deng. A construction of $ p $-ary linear codes with two or three weights. Advances in Mathematics of Communications, 2021, 15 (1) : 9-22. doi: 10.3934/amc.2020039 |
[15] |
Tingting Wu, Li Liu, Lanqiang Li, Shixin Zhu. Repeated-root constacyclic codes of length $ 6lp^s $. Advances in Mathematics of Communications, 2021, 15 (1) : 167-189. doi: 10.3934/amc.2020051 |
[16] |
Wenjun Liu, Yukun Xiao, Xiaoqing Yue. Classification of finite irreducible conformal modules over Lie conformal algebra $ \mathcal{W}(a, b, r) $. Electronic Research Archive, , () : -. doi: 10.3934/era.2020123 |
[17] |
Linglong Du, Min Yang. Pointwise long time behavior for the mixed damped nonlinear wave equation in $ \mathbb{R}^n_+ $. Networks & Heterogeneous Media, 2020 doi: 10.3934/nhm.2020033 |
[18] |
Kaixuan Zhu, Ji Li, Yongqin Xie, Mingji Zhang. Dynamics of non-autonomous fractional reaction-diffusion equations on $ \mathbb{R}^{N} $ driven by multiplicative noise. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020376 |
[19] |
Ivan Bailera, Joaquim Borges, Josep Rifà. On Hadamard full propelinear codes with associated group $ C_{2t}\times C_2 $. Advances in Mathematics of Communications, 2021, 15 (1) : 35-54. doi: 10.3934/amc.2020041 |
[20] |
Federico Rodriguez Hertz, Zhiren Wang. On $ \epsilon $-escaping trajectories in homogeneous spaces. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 329-357. doi: 10.3934/dcds.2020365 |
2019 Impact Factor: 0.734
Tools
Metrics
Other articles
by authors
[Back to Top]