A stability result and a spectrum result on constant dimension codes

Lisa Hernandez Lucas; Ivan  Landjev; Leo Storme; Peter Vandendriessche

doi:10.1016/j.laa.2021.03.019

A stability result and a spectrum result on constant dimension codes

Lisa Hernandez Lucas, Ivan Landjev, Leo Storme, Peter Vandendriessche

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2 Citations (Scopus)

Abstract

In this paper we continue the study of subspace codes with constant intersection dimension (SCIDs). We investigate the largest possible dimensions spanned by non-sunflower SCIDs, by proving a stability result and we present a spectrum result giving us a large interval for the dimensions that can be generated by non-sunflower SCIDs. We also prove that SCIDs are in fact equivalent to linear spaces and give some results regarding this equivalence, including an improvement to a result by E. Gorla and A. Ravagnani, regarding the number of centers of a SCID.

Original language	English
Article number	621
Pages (from-to)	193-213
Number of pages	21
Journal	Linear Algebra and its Applications
Volume	621
DOIs	https://doi.org/10.1016/j.laa.2021.03.019 https://doi.org/10.1016/j.laa.2021.03.019
Publication status	Published - 15 Jul 2021

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title = "A stability result and a spectrum result on constant dimension codes",

abstract = "In this paper we continue the study of subspace codes with constant intersection dimension (SCIDs). We investigate the largest possible dimensions spanned by non-sunflower SCIDs, by proving a stability result and we present a spectrum result giving us a large interval for the dimensions that can be generated by non-sunflower SCIDs. We also prove that SCIDs are in fact equivalent to linear spaces and give some results regarding this equivalence, including an improvement to a result by E. Gorla and A. Ravagnani, regarding the number of centers of a SCID.",

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AU - Hernandez Lucas, Lisa

AU - Landjev, Ivan

AU - Storme, Leo

AU - Vandendriessche, Peter

PY - 2021/7/15

Y1 - 2021/7/15

N2 - In this paper we continue the study of subspace codes with constant intersection dimension (SCIDs). We investigate the largest possible dimensions spanned by non-sunflower SCIDs, by proving a stability result and we present a spectrum result giving us a large interval for the dimensions that can be generated by non-sunflower SCIDs. We also prove that SCIDs are in fact equivalent to linear spaces and give some results regarding this equivalence, including an improvement to a result by E. Gorla and A. Ravagnani, regarding the number of centers of a SCID.

AB - In this paper we continue the study of subspace codes with constant intersection dimension (SCIDs). We investigate the largest possible dimensions spanned by non-sunflower SCIDs, by proving a stability result and we present a spectrum result giving us a large interval for the dimensions that can be generated by non-sunflower SCIDs. We also prove that SCIDs are in fact equivalent to linear spaces and give some results regarding this equivalence, including an improvement to a result by E. Gorla and A. Ravagnani, regarding the number of centers of a SCID.

KW - Subspace codes

KW - Sunflower

KW - Subspace codes with constant intersection dimension

KW - Linear spaces

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DO - 10.1016/j.laa.2021.03.019

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VL - 621

SP - 193

EP - 213

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

M1 - 621

ER -

A stability result and a spectrum result on constant dimension codes

Abstract

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