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On the lengths of divisible codes

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. 4051-4060.
ISSN 0018-9448
DOI: https://doi.org/10.1109/TIT.2020.2968832

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 another language

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 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.uni-bayreuth.de/id/eprint/55583