Consistent Flag Codes

Alonso-González, Clementa; Navarro-Pérez, Miguel Ángel

doi:10.3390/math8122234

Cited by 7 publications

(29 citation statements)

References 11 publications

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“…. , t r ), n) can be endowed with a metric by a natural extension of the injection distance defined in (2). More precisely, given two flags…”

Section: Subspace Codes and Flag Codesmentioning

confidence: 99%

“…In this context, collections of flags are denominated flag codes and they appear as a generalization of constant dimension codes. The recent works [2,4,5,6,13] among others, show a growing interest in this topic.…”

Section: Introductionmentioning

confidence: 99%

“…In the study of flag codes, a central problem is the one of unraveling to what extent is it possible to get the parameters of a flag code from the ones of its projected codes and conversely. In [3,5,6,15] this problem has been addressed for the family of flag codes attaining the maximum distance (optimum distance flag codes) whereas in [2], the authors define consistent flag codes as precisely those ones whose projected codes completely determine their parameters. In the paper at hand, we deal with this question for general full flag codes from an innovative combinatorial perspective.…”

Section: Introductionmentioning

confidence: 99%

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A Combinatorial Approach to Flag Codes

Alonso-González¹,

Navarro-Pérez²

2021

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In network coding, a flag code is a collection of flags, that is, sequences of nested subspaces of a vector space over a finite field. Due to its definition as the sum of the corresponding subspace distances, the flag distance parameter encloses a hidden combinatorial structure. To bring it to light, in this paper, we interpret flag distances by means of distance paths drawn in a convenient distance support. The shape of such a support allows us to create an ad hoc associated Ferrers diagram frame where we develop a combinatorial approach to flag codes by relating the possible realizations of their minimum distance to different partitions of appropriate integers. This novel viewpoint permits to establish noteworthy connections between the flag code parameters and the ones of its projected codes in terms of well known concepts coming from the classical partitions theory.

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“…. , t r ), n) can be endowed with a metric by a natural extension of the injection distance defined in (2). More precisely, given two flags…”

Section: Subspace Codes and Flag Codesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Combinatorial Approach to Flag Codes

Alonso-González¹,

Navarro-Pérez²

2021

Preprint

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“…In [2] the authors introduced a family of flag codes such that the distance and size of the projected codes completely determine the ones of the corresponding flag code. Definition 3.4.…”

Section: Flags and Flag Codesmentioning

confidence: 99%

“…In the network coding context, they appeared for the first time in the paper [15] where the multiplicative action of GL(n, q) is translated from subspaces to flags to provide different constructions of orbit flag codes. This seminal work has sparked an incipient interest in flag codes reflected in the recent works [2,3,4,6,5,7,14,19].…”

Section: Introductionmentioning

confidence: 99%

On Generalized Galois Cyclic Orbit Flag Codes

Alonso-González¹,

Navarro-Pérez²

2021

Preprint

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Flag codes that are orbits of a cyclic subgroup of the general linear group acting on flags of a vector space over a finite field, are called cyclic orbit flag codes. In this paper we present a new contribution to the study of such codes started in [3], by focusing this time on the generating flag. More precisely, we examine those ones whose generating flag has at least one subfield among its subspaces. In this situation, two important families arise: the already known Galois flag codes, in case we have just fields, or the generalized Galois flag codes in other case. We investigate the parameters and properties of the latter ones and explore the relationship with their underlying Galois flag code.

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