A bound-achieving modified Etzion-Vardy (5, 3) projective space code

Ghatak, Anirban

doi:10.1109/ncc.2016.7561182

Cited by 2 publications

(4 citation statements)

References 11 publications

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“…The replacements are chosen only among vectors which preserve the Schubert cell signature of each subspace. The details of constructing the MEV (modified EV) code have been given in [18] and are briefly recounted here for completeness. The line l 2 (S1) is a subspace of the orthogonal complement of the line l 5 (S2); hence it was attempted to modify either of them by changing a single vector at a time.…”

Section: A the Minimal Change Strategy: Mev Code And Its Dualmentioning

confidence: 99%

“…The authors have shown that the basic building blocks of these codes are maximal partial spreads of 2-dimensional subspaces in a 5dimensional ambient space. An optimal (5, 3) 2 projective space code was reported in [18], which was obtained by a strategy of minimal changes to a nearly optimal code given by Etzion-Vardy in [13]. Both the Etzion-Vardy (EV) code and the optimal variant can be described in terms of maximal partial spreads of 2-dimensional subspaces.…”

Section: Introductionmentioning

confidence: 99%

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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: A the Minimal Change Strategy: Mev Code And Its Dualmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Ghatak

2017

Preprint

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“…Another approach ( for instance, in [8,12,13]) involves puncturing known constant dimension codes and adding suitable subspaces to increase the overall code-size. An optimal binary (5, 3) projective space code was reported in [14], which was obtained by a strategy of minimal changes to the nearly optimal code given by Etzion and Vardy in [7]. Both the Etzion-Vardy (EV) code and the optimal variant can be described in terms of maximal partial spreads of 2-dimensional (vector) subspaces in a 5-dimensional ambient (vector) space.…”

Section: Introductionmentioning

confidence: 99%

“…If we consider the associated projective geometry PG(4, 2), the 2-subspaces and 3-subspaces are the lines and planes of the geometry, respectively. In obtaining the optimal code in [14], results from the classification of maximal partial line spreads of PG (4,2), as presented in [15] (cf. [13,16]), were used.…”

Section: Introductionmentioning

confidence: 99%

Intersection Patterns in Optimal Binary $(5,3)$ Doubling Subspace Codes

Ghatak¹,

Mukherjee²

2021

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Subspace codes are collections of subspaces of a projective space such that any two subspaces satisfy a pairwise minimum distance criterion. There exists a significant body of research on subspace codes, especially with regard to their application for error and erasure correction in random networks. Recent results have shown that it is possible to construct optimal (5, 3) subspace codes from pairs of partial spreads in the projective space PG(4, q) over the finite fields F q , termed doubling codes. In this context, we have utilized a complete classification of maximal partial line spreads in PG(4, 2) in literature to establish the types of the spreads in the doubling code instances obtained from two recent constructions of optimum (5, 3) q codes, restricted to F 2 . Further we present a new characterization of a subclass of doubling codes based on the intersection patterns of key subspaces in the pair of constituent spreads. This characterization is a first step towards identifying all possible spread pairs that can yield optimal (5, 3) 2 doubling codes.

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A bound-achieving modified Etzion-Vardy (5, 3) projective space code

Cited by 2 publications

References 11 publications

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

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

Intersection Patterns in Optimal Binary $(5,3)$ Doubling Subspace Codes

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