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Combining subspace codes
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 |
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