An Orbital Construction of Optimum Distance Flag Codes

11/05/2020

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by   Clementa Alonso-González, et al.

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Flag codes are multishot network codes consisting of sequences of nested subspaces (flags) of a vector space 𝔽_q^n, where q is a prime power and 𝔽_q, the finite field of size q. In this paper we study the construction on 𝔽_q^2k of full flag codes having maximum distance (optimum distance full flag codes) that can be endowed with an orbital structure provided by the action of a subgroup of the general linear group. More precisely, starting from a subspace code of dimension k and maximum distance with a given orbital description, we provide sufficient conditions to get an optimum distance full flag code on 𝔽_q^2k having an orbital structure directly induced by the previous one. In particular, we exhibit a specific orbital construction with the best possible size from an orbital construction of a planar spread on 𝔽_q^2k that strongly depends on the characteristic of the field.