[1]
|
R. Ahlswede, N. Cai, R. Li and R. W. Yeung, Network information flow, IEEE Trans. Inform. Theory, 46 (2000), 1204-1216.
doi: 10.1109/18.850663.
|
[2]
|
R. Baer, Linear Algebra and Projective Geometry, Academic Press Inc., New York, 1952.
|
[3]
|
F. Bardestani and A. Iranmanesh, Cyclic orbit codes with the normalizer of a singer subgroup, J. Sci. Islam. Repub. Iran, 26 (2015), 49-55.
|
[4]
|
E. Biglieri and M. Elia, Multidimensional modulation and coding for band-limited digital channels, IEEE Trans. Inform. Theory, 34 (1988), 803-809.
doi: 10.1109/18.9777.
|
[5]
|
A. R. Calderbank, Multilevel codes and multistage decoding, IEEE Trans. Comm., 37 (1989), 222-229.
doi: 10.1109/26.20095.
|
[6]
|
B. Chen and H. Liu, Constructions of cyclic constant dimension codes, Des. Codes Cryptogr., 86 (2018), 1267-1279.
doi: 10.1007/s10623-017-0394-9.
|
[7]
|
J.-J. Climent, V. Requena and X. S.-Escrivà, A construction of Abelian non-cyclic orbit codes, Cryptogr. Commun., 11 (2019), 839-852.
doi: 10.1007/s12095-018-0306-5.
|
[8]
|
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Fundamental Principles of Mathematical Sciences, 290, Springer-Verlag, New York, 1999.
doi: 10.1007/978-1-4757-6568-7.
|
[9]
|
P. Delsarte, Bilinear forms over a finite field, with applications to coding theory, J. Combin. Theory Ser. A, 25 (1978), 226-241.
doi: 10.1016/0097-3165(78)90015-8.
|
[10]
|
T. Etzion and A. Vardy, Error-correcting codes in projective space, IEEE Trans. Inform. Theory, 57 (2011), 1165-1173.
doi: 10.1109/TIT.2010.2095232.
|
[11]
|
G. Forney Jr., Geometrically uniform codes, IEEE Trans. Inform. Theory, 37 (1991), 1241-1260.
doi: 10.1109/18.133243.
|
[12]
|
È. M. Gabidulin, Theory of codes with maximum rank distance, Problemy Peredachi Informatsii, 21 (1985), 3-16.
|
[13]
|
J. T. Goozeff, Abelian p-subgroups of the general linear group, J. Austral. Math. Soc., 11 (1970), 257-259.
doi: 10.1017/S1446788700006613.
|
[14]
|
D. Heinlein, M. Kiermaier, S. Kurz and A. Wassermann, Tables of subspace codes, preprint, arXiv: 1601.02864.
|
[15]
|
H. Imai and S. Hirakawa, A new multilevel coding method using error-correcting codes, IEEE Trans. Inform. Theory, 23 (1977), 371-377.
doi: 10.1109/TIT.1977.1055718.
|
[16]
|
I. M. Isaacs, Finite Group Theory, Graduate Studies in Mathematics, 92, American Mathematical Society, Providence, RI, 2008.
doi: 10.1090/gsm/092.
|
[17]
|
A. Khaleghi, D. Silva and F. R. Kschischang, Subspace codes, in Cryptography and Coding, Lecture Notes in Comput. Sci., 5921, Springer, Berlin, 2009, 1-21.
doi: 10.1007/978-3-642-10868-6_1.
|
[18]
|
R. Köetter and F. R. Kschischang, Coding for errors and erasures in random network coding, IEEE Trans. Inform. Theory, 54 (2008), 3579-3591.
doi: 10.1109/TIT.2008.926449.
|
[19]
|
A. Kohnert and S. Kurz, Construction of large constant dimension codes with a prescribed minimum distance, in Mathematical Methods in Computer Science, Lecture Notes in Comput. Sci., 5393, Springer, Berlin, 2008, 31-42.
doi: 10.1007/978-3-540-89994-5_4.
|
[20]
|
H. A. Loeliger, Signal sets matched to groups, IEEE Trans. Inform. Theory, 37 (1991), 1675-1682.
doi: 10.1109/18.104333.
|
[21]
|
H. G-Luerssen, K. Morrison and C. Troha, Cyclic orbit codes and stabilizer subfields, Adv. Math. Commun., 9 (2015), 177-197.
doi: 10.3934/amc.2015.9.177.
|
[22]
|
F. Manganiello, E. Gorla and J. Rosenthal, Spread codes and spread decoding in network coding, IEEE International Symposium on Information Theory, (2008), 881-885.
doi: 10.1109/ISIT.2008.4595113.
|
[23]
|
R. W. Nobrega and B. F. Uchoa-Filho, Multishot codes for network coding: Bounds and a multilevel construction, IEEE International Symposium on Information Theory, (2009), 428-432.
doi: 10.1109/ISIT.2009.5205750.
|
[24]
|
J. J. Rotman, An Introduction to the Theory of Groups, Graduate Texts in Mathematics, 148, Springer-Verlag, New York, 1995.
doi: 10.1007/978-1-4612-4176-8.
|
[25]
|
D. Slepian, Group codes for the Gaussian channel, Bell System Tech. J., 47 (1968), 575-602.
doi: 10.1002/j.1538-7305.1968.tb02486.x.
|
[26]
|
D. A. Suprunenko, Matrix Groups, Translations of Mathematical Monographs, 45, American Mathematical Society, Providence, RI, 1976.
|
[27]
|
A.-L. Trautmann, Isometry and automorphisms of constant dimension codes, Adv. Math. Commun., 7 (2013), 147-160.
doi: 10.3934/amc.2013.7.147.
|
[28]
|
A.-L. Trautmann, F. Manganiello, M. Braun and J. Rosenthal, Cyclic orbit codes, IEEE Trans. Inform. Theory, 59 (2013), 7386-7404.
doi: 10.1109/TIT.2013.2274266.
|
[29]
|
A.-L. Trautmann, F. Manganiello and J. Rosenthal, Orbit codes - A new concept in the area of network coding, IEEE Information Theory Workshop, Dublin, Ireland, 2010, 1-4.
doi: 10.1109/CIG.2010.5592788.
|
[30]
|
Z. Wan, On geometrically uniform signal sets and signal sets matched to groups, IEEE International Symposium on Information Theory, San Antonio, 1993,179pp.
doi: 10.1109/ISIT.1993.748493.
|