Title data
Kiermaier, Michael ; Kurz, Sascha:
On the lengths of divisible codes.
In: IEEE Transactions on Information Theory.
Vol. 66
(July 2020)
Issue 7
.
 pp. 40514060.
ISSN 00189448
DOI: https://doi.org/10.1109/TIT.2020.2968832
Project information
Project title: 



Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract in another language
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:  Article in a journal 

Refereed:  Yes 
Keywords:  divisible codes; constant dimension codes; partial spreads 
Subject classification:  Mathematics Subject Classification Code: 51E23 (05B40) 
Institutions of the University:  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 
Result of work at the UBT:  Yes 
DDC Subjects:  000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics 
Date Deposited:  23 Jun 2020 06:52 
Last Modified:  23 Jun 2020 06:52 
URI:  https://eref.unibayreuth.de/id/eprint/55583 