Year: 2020
Type: article
Abstract: In this article, the effective lengths of all qr-divisible linear codes over Fqwith a non-negative integer r are determined. For that purpose, the Sq(r)-adic expansion of an integer n is introduced. It is shown that there exists a qr-divisible Fq-linear code of effective length n if and only if the leading coefficient of the Sq(r)-adic expansion of n is non-negative. Furthermore, the maximum weight of a qr-divisible code of effective length n is at most σqr, where σ denotes the cross-sum of the Sq(r)-adic expansion of n. This result has applications in Galois geometries. A recent theorem of Nästase 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.
Authors: Michael Kiermaier, Sascha Kurz
Institution: University of Bayreuth
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G6624215543
OpenAlex ID: W2904347558