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Degenerate flag varieties in network coding
RWTH Aachen University, 52056 Aachen, Germany |
Building upon the application of flags to network coding introduced in [
References:
| [1] |
G. Cerulli Irelli, X. Fang, E. Feigin, G. Fourier and R. Reineke,
Linear degenerations of flag varieties, Math. Z., 287 (2017), 615-654.
doi: 10.1007/s00209-016-1839-y. |
| [2] |
E. Feigin,
$\mathbb{G}_a^M$ degeneration of flag varieties, Selecta Math. (N.S.), 18 (2012), 513-537.
doi: 10.1007/s00029-011-0084-9. |
| [3] |
E. Feigin, G. Fourier and P. Littelmann,
PBW filtration and bases for irreducible modules in type $ {\mathbb{A}} _n$, Transform. Groups, 16 (2011), 71-89.
doi: 10.1007/s00031-010-9115-4. |
| [4] |
G. C. Irelli and M. Lanini,
Degenerate flag varieties of type $ {\mathbb{A}} $ and $ {\mathbb{C}} $ are schubert varieties, Int. Math. Research Notices, 2015 (2015), 6353-6374.
doi: 10.1093/imrn/rnu128. |
| [5] |
R. Kötter and F. R. Kschischang,
Coding for errors and erasures in random network coding, IEEE Trans. Inform., 54 (2008), 3579-3591.
doi: 10.1109/TIT.2008.926449. |
| [6] |
D. Liebhold, G. Nebe and A. Vazquez-Castro,
Network coding with flags, Des. Codes Cryptogr., 86 (2018), 269-284.
doi: 10.1007/s10623-017-0361-5. |
| [7] |
D. Liebhold, Flag Codes With Application to Network Coding, PhD Thesis, RWTH Aachen 2019. |
| [8] |
A. Ravagnani,
Rank-metric codes and their duality theory, Des. Codes Cryptogr., 80 (2016), 197-216.
doi: 10.1007/s10623-015-0077-3. |
| [9] |
D. Silva, F. R. Kschischang and R. Kötter,
A rank-metric approach to error control in random network coding, IEEE Trans. Inform. Theory, 54 (2008), 3951-3967.
doi: 10.1109/TIT.2008.928291. |
show all references
References:
| [1] |
G. Cerulli Irelli, X. Fang, E. Feigin, G. Fourier and R. Reineke,
Linear degenerations of flag varieties, Math. Z., 287 (2017), 615-654.
doi: 10.1007/s00209-016-1839-y. |
| [2] |
E. Feigin,
$\mathbb{G}_a^M$ degeneration of flag varieties, Selecta Math. (N.S.), 18 (2012), 513-537.
doi: 10.1007/s00029-011-0084-9. |
| [3] |
E. Feigin, G. Fourier and P. Littelmann,
PBW filtration and bases for irreducible modules in type $ {\mathbb{A}} _n$, Transform. Groups, 16 (2011), 71-89.
doi: 10.1007/s00031-010-9115-4. |
| [4] |
G. C. Irelli and M. Lanini,
Degenerate flag varieties of type $ {\mathbb{A}} $ and $ {\mathbb{C}} $ are schubert varieties, Int. Math. Research Notices, 2015 (2015), 6353-6374.
doi: 10.1093/imrn/rnu128. |
| [5] |
R. Kötter and F. R. Kschischang,
Coding for errors and erasures in random network coding, IEEE Trans. Inform., 54 (2008), 3579-3591.
doi: 10.1109/TIT.2008.926449. |
| [6] |
D. Liebhold, G. Nebe and A. Vazquez-Castro,
Network coding with flags, Des. Codes Cryptogr., 86 (2018), 269-284.
doi: 10.1007/s10623-017-0361-5. |
| [7] |
D. Liebhold, Flag Codes With Application to Network Coding, PhD Thesis, RWTH Aachen 2019. |
| [8] |
A. Ravagnani,
Rank-metric codes and their duality theory, Des. Codes Cryptogr., 80 (2016), 197-216.
doi: 10.1007/s10623-015-0077-3. |
| [9] |
D. Silva, F. R. Kschischang and R. Kötter,
A rank-metric approach to error control in random network coding, IEEE Trans. Inform. Theory, 54 (2008), 3951-3967.
doi: 10.1109/TIT.2008.928291. |
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