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On the lengths of divisible codes

URN to cite this document: urn:nbn:de:bvb:703-epub-4304-1

Title data

Kiermaier, Michael ; Kurz, Sascha:
On the lengths of divisible codes.
Bayreuth , 2019 . - 17 S.

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Project information

Project title:
Project's official titleProject's id
Integer Linear Programming Models for Subspace Codes and Finite GeometryNo information

Project financing: Deutsche Forschungsgemeinschaft

Abstract

In this article, the effective lengths of all q^r-divisible linear codes over GF(q) with a non-negative integer r are determined. For that purpose, the S_q(r)-adic expansion of an integer n is introduced. It is shown that there exists a q^r-divisible GF(q)-linear code of effective length n if and only if the leading coefficient of the S_q(r)-adic expansion of n is non-negative. Furthermore, the maximum weight of a q^r-divisible code of effective length n is at most the cross-sum of the S_q(r)-adic expansion of n. This result has applications in Galois geometries. A recent theorem of Nastase and Sissokho on the maximum sizes of partial spreads follows as a corollary. Furthermore, we get an improvement of the Johnson bound for constant dimension subspace codes.

Further data

Item Type: Preprint, postprint
Keywords: divisible codes; constant dimension codes; partial spreads
Subject classification: Mathematics Subject Classification Code: 51E23 (05B40)
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 Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics in Economy > Chair Mathematics in Economy - Univ.-Prof. Dr. Jörg Rambau
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-4304-1
Date Deposited: 03 Apr 2019 12:22
Last Modified: 03 Apr 2019 12:22
URI: https://epub.uni-bayreuth.de/id/eprint/4304

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