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Title data
Kiermaier, Michael ; Kurz, Sascha:
On the lengths of divisible codes.
Bayreuth
,
2019
. - 17 S.
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Project information
| Project title: |
Project's official title Project's id Integer Linear Programming Models for Subspace Codes and Finite Geometry No information |
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| Project financing: |
Deutsche Forschungsgemeinschaft |
Abstract
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 sizes of partial spreads follows as a corollary. Furthermore, we get an improvement of the Johnson bound for constant dimension subspace codes.
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- On the lengths of divisible codes. (deposited 03 Apr 2019 12:22) [Currently Displayed]
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