May  2015, 9(2): 177-197. doi: 10.3934/amc.2015.9.177

Cyclic orbit codes and stabilizer subfields

1. 

University of Kentucky, Department of Mathematics, Lexington, KY 40506-0027

2. 

School of Mathematical Sciences, University of Northern Colorado, Greeley, CO 80639, United States

3. 

Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, United States

Received  March 2014 Published  May 2015

Cyclic orbit codes are constant dimension subspace codes that arise as the orbit of a cyclic subgroup of the general linear group acting on subspaces in the given ambient space. With the aid of the largest subfield over which the given subspace is a vector space, the cardinality of the orbit code can be determined, and estimates for its distance can be found. This subfield is closely related to the stabilizer of the generating subspace. Finally, with a linkage construction larger, and longer, constant dimension codes can be derived from cyclic orbit codes without compromising the distance.
Citation: Heide Gluesing-Luerssen, Katherine Morrison, Carolyn Troha. Cyclic orbit codes and stabilizer subfields. Advances in Mathematics of Communications, 2015, 9 (2) : 177-197. doi: 10.3934/amc.2015.9.177
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show all references

References:
[1]

IEEE Trans. Inf. Theory, IT-46 (2000), 1204-1216. doi: 10.1109/18.850663.  Google Scholar

[2]

M. Braun, T. Etzion, P. Östergård, A. Vardy and A. Wassermann, Existence of $q$-analogs of Steiner systems,, preprint, ().   Google Scholar

[3]

Des. Codes Crypt., 54 (2010), 101-107. doi: 10.1007/s10623-009-9311-1.  Google Scholar

[4]

in Proc. 19th Int. Symp. Math. Theory Netw. Syst., Budapest, Hungary, 2010, 1811-1814. Google Scholar

[5]

IEEE Trans. Inf. Theory, IT-55 (2009), 2909-2919. doi: 10.1109/TIT.2009.2021376.  Google Scholar

[6]

IEEE Trans. Inf. Theory, IT-57 (2011), 1165-1173. doi: 10.1109/TIT.2010.2095232.  Google Scholar

[7]

Adv. Math. Commun., 5 (2011), 161-176. doi: 10.3934/amc.2011.5.161.  Google Scholar

[8]

Probl. Inf. Transm., 21 (1985), 1-12.  Google Scholar

[9]

Probl. Inf. Trans. (Engl. Transl.), 46 (2010), 300-320. doi: 10.1134/S0032946010040034.  Google Scholar

[10]

in Proc. 12th IMA Conf. Crypt. Coding, Cirencester, 2009, 1-21. doi: 10.1007/978-3-642-10868-6_1.  Google Scholar

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IEEE Trans. Inf. Theory, IT-54 (2008), 3579-3591. doi: 10.1109/TIT.2008.926449.  Google Scholar

[12]

in Mathematical Methods in Computer Science (eds. J. Calmet, W. Geiselmann and J. Müller-Quade), Springer, Berlin, 2008, 31-42. doi: 10.1007/978-3-540-89994-5_4.  Google Scholar

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[14]

IEEE Trans. Inf. Theory, IT-54 (2008), 3951-3967. doi: 10.1109/TIT.2008.928291.  Google Scholar

[15]

Adv. Math. Commun., 7 (2013), 147-160. doi: 10.3934/amc.2013.7.147.  Google Scholar

[16]

IEEE Trans. Inf. Theory, IT-59 (2013), 7386-7404. doi: 10.1109/TIT.2013.2274266.  Google Scholar

[17]

Des. Codes Crypt., 50 (2009), 163-172. doi: 10.1007/s10623-008-9221-7.  Google Scholar

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