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Projective divisible binary codes

URN to cite this document: urn:nbn:de:bvb:703-epub-3255-3

Title data

Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Projective divisible binary codes.
Bayreuth , 2017 . - 10 S.

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Project's official title
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Integer Linear Programming Models for Subspace Codes and Finite Geometry
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Project financing: Deutsche Forschungsgemeinschaft


For which positive integers n, k, and r does there exist a linear [n,k] code C over GF(q) with all codeword weights divisible by q^r and such that the columns of a generating matrix of C are projectively distinct? The motivation for studying this problem comes from the theory of partial spreads, or subspace codes with the highest possible minimum distance, since the set of holes of a partial spread of r-flats in PG(v-1,GF(q)) corresponds to a q^r-divisible code with k <= v. In this paper we provide an introduction to this problem and report on new results for the binary case q=2.

Abstract in another language

Für welche positiven ganzen Zahlen n, k und r gibst es einen linearen [n,k] Code C über GF(q) bei dem die Gewichte aller Codewörter durch q^r teilbar sind und die Spalten der Generatormatrix von C projektiv verschieden sind? Die Motivation für diese Fragestellung kommt aus der Theorie der partial spreads bzw. Teilraumcodes mit der größtmöglichen Minimaldistanz. Der Zusammenhang ist gegeben durch die Tatsache, dass die sogenannten Löcher eines partial r-spreads in PG(v-1,GF(q)) einem q^r-teilbaren Code mit k <= v entsprechen. Hier betrachten wir den binären Fall q=2 und geben eine Einführung in die Fragestellung der Existenz q^r-teilbarer linearer Codes.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erschienen in:
Augot, Daniel ; Krouk, Evgeny ; Loidreau, Pierre (Hrsg.): The Tenth International Workshop on Coding and Cryptography 2017 : WCC Proceedings. - Saint-Petersburg , 2017 . - 10 S.
Keywords: divisible codes; projective codes; partial spreads
Subject classification: Mathematics Subject Classification Code: 94B05 (51E23)
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics
Faculties > Faculty of Mathematics, Physics und Computer Science
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-3255-3
Date Deposited: 24 Mar 2017 09:41
Last Modified: 27 May 2021 08:39


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