A Construction of Orbit Codes

Climent, Joan‐Josep; Requena, Verónica; Soler–Escrivà, Xaro

doi:10.1007/978-3-319-66278-7_7

Cited by 3 publications

(2 citation statements)

References 16 publications

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“…The maximum values of k and n which we can choose in our construction, satisfying equation 8are k = p r−1 (p − 1) and n = p r−1 (2p − 1). A preliminary version for r = 1 was presented at the 5th International Castle Meeting on Coding Theory and Applications [5].…”

Section: Our Constructionmentioning

confidence: 99%

A construction of Abelian non-cyclic orbit codes

2018

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A constant dimension code consists of a set of k-dimensional subspaces of F n q , where F q is a finite field of q elements. Orbit codes are constant dimension codes which are defined as orbits under the action of a subgroup of the general linear group on the set of all k-dimensional subspaces of F n q. If the acting group is Abelian, we call the corresponding orbit code Abelian orbit code. In this paper we present a construction of an Abelian non-cyclic orbit code for which we compute its cardinality and its minimum subspace distance. Our code is a partial spread and consequently its minimum subspace distance is maximal.

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Section: Our Constructionmentioning

confidence: 99%

A construction of Abelian non-cyclic orbit codes

2018

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“…If G is cyclic, then some authors speak of cyclic orbit codes, see e.g. [12,35,36,55,79]. For these objects one can utilize the theory of subspace polynomials, see [7,71], and Sidon spaces, see [72].…”

Section: Codes With Prescribed Automorphismsmentioning

confidence: 99%

Tables of subspace codes

Heinlein,

Kiermaier,

Kurz

et al. 2016

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The main problem of subspace coding asks for the maximum possible cardinality of a subspace code with minimum distance at least d over F n q , where the dimensions of the codewords, which are vector spaces, are contained in K ⊆ {0, 1, . . . , n}. In the special case of K = {k} one speaks of constant dimension codes. Since this emerging field is very prosperous on the one hand side and there are a lot of connections to classical objects from Galois geometry it is a bit difficult to keep or to obtain an overview about the current state of knowledge. To this end we have implemented an on-line database of the (at least to us) known results at subspacecodes.uni-bayreuth.de. The aim of this technical report is to provide a user guide how this technical tool can be used in research projects and to describe the so far implemented theoretic and algorithmic knowledge.

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