Title data
Kiermaier, Michael ; Kurz, Sascha:
On the lengths of divisible codes.
Bayreuth
,
2020
.  17 S.
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Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract
In this article, the effective lengths of all q^rdivisible linear codes over GF(q) with a nonnegative 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^rdivisible 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 nonnegative. Furthermore, the maximum weight of a q^rdivisible code of effective length n is at most the crosssum 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 size of a partial spread 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 Faculties > Faculty of Mathematics, Physics und Computer Science 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 (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics 
Language:  English 
Originates at UBT:  No 
URN:  urn:nbn:de:bvb:703epub46026 
Date Deposited:  31 Jan 2020 10:45 
Last Modified:  31 Jan 2020 10:47 
URI:  https://epub.unibayreuth.de/id/eprint/4602 
Available Versions of this Item

On the lengths of divisible codes. (deposited 03 Apr 2019 12:22)
 On the lengths of divisible codes. (deposited 31 Jan 2020 10:45) [Currently Displayed]