Title data
Kiermaier, Michael ; Kurz, Sascha:
On the lengths of divisible codes.
Bayreuth
,
2019
.  17 p.
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 sizes of partial spreads follows as a corollary. Furthermore, we get an improvement of the Johnson bound for constant dimension subspace codes.