Construction of Subspace Codes through Linkage

Gluesing-Luerssen, Heide; Troha, Carolyn

doi:10.48550/arxiv.1505.02186

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2017

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“…The notion of subspace coding for errors and erasures in random networks was introduced in the papers of Kötter et al ( [1], [2]). There exists a rich body of literature dealing with the encoding and decoding of constant dimension codes, (for instance, references [3] - [11]) where all the codeword subspaces have the same dimension. An extensive list of open problems in this field and relevant references are to be found in Etzion's survey [12].…”

Section: Introductionmentioning

confidence: 99%

Optimal Binary $(5,3)$ Projective Space Codes from Maximal Partial Spreads

Ghatak

2017

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Recently a construction of optimal non-constant dimension subspace codes, also termed projective space codes, has been reported in a paper of Honold-Kiermaier-Kurz. Restricted to binary codes in a 5-dimensional ambient space with minimum subspace distance 3, these optimal codes may be interpreted in terms of maximal partial spreads of 2-dimensional subspaces. In a parallel development, an optimal binary (5, 3) code was obtained by a minimal change strategy on a nearly optimal example of Etzion and Vardy. In this paper, we report several examples of optimal binary (5, 3) codes obtained by the application of this strategy combined with changes to the spread structure of existing codes. We also establish that all our examples lie outside the framework of the construction of Honold et al.

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Section: Introductionmentioning

confidence: 99%

Optimal Binary $(5,3)$ Projective Space Codes from Maximal Partial Spreads

Ghatak

2017

Preprint

View full text Add to dashboard Cite

show abstract

Construction of Subspace Codes through Linkage

Cited by 1 publication

References 0 publications

Optimal Binary $(5,3)$ Projective Space Codes from Maximal Partial Spreads

Optimal Binary $(5,3)$ Projective Space Codes from Maximal Partial Spreads

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