On MSR subspace families of lines

Ferdinand Ihringer

doi:10.3934/amc.2023052

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2025, Volume 19, Issue 1: 219-226. Doi: 10.3934/amc.2023052

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On MSR subspace families of lines

Ferdinand Ihringer

Dept. of Mathematics: Analysis, Logic and Discrete Math., Ghent University, Belgium

Received: May 2023

Revised: October 2023

Early access: November 2023

Published: February 2025

The author was supported by a postdoctoral fellowship of the Research Foundation – Flanders (FWO) during the work on this document.

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Abstract

A minimum storage regenerating (MSR) subspace family of $ {\mathbb F}_q^{2m} $ is a set $ {\mathcal S} $ of $ m $-spaces in $ {\mathbb F}_q^{2m} $ such that for any $ m $-space $ S $ in $ {\mathcal S} $ there exists an element in $ \mathrm{PGL}(2m, q) $ which maps $ S $ to a complement and fixes $ {\mathcal S} \setminus \{ S \} $ element-wise. We show that an MSR subspace family of $ 2 $-spaces in $ {\mathbb F}_q^4 $ has at most size $ 6 $ with equality if and only if it is a particular subset of a Segre variety. This implies that an $ (k{+}2, k, 4) $-MSR code has $ k \leq 7 $.

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Mathematics Subject Classification: Primary: 94B05, 51E23.

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References

[1]	O. Alrabiah and V. Guruswami, An exponential lower bound on the sub-packetization of MSR codes, IEEE Trans. Inform. Theory, 67 (2021), 8086-8093. doi: 10.1109/TIT.2021.3112286.
[2]	M. Lavrauw and C. Zanella, Subspaces intersecting each element of a regulus in one point, André-Bruck-Bose representation and clubs, Electron. J. Combin., 23 (2016), Paper 1.37, 11 pp. doi: 10.37236/4662.
[3]	I. Tamo, Z. Wang and J. Bruck, Access versus bandwidth in codes for storage, IEEE Trans. Inform. Theory, 60 (2014), 2028-2037. doi: 10.1109/TIT.2014.2305698.
[4]	D. E. Taylor, The Geometry of the Classical Groups, Heldermann, Berlin, 1992.
[5]	Z. Wang, I. Tamo and J. Bruck, Long MDS codes for optimal repair bandwidth, In Proc. of 2012 IEEE International Symposium on Information Theory (ISIT) (2012), 182-1186. doi: 10.1109/ISIT.2012.6283041.