Publication:
An orbital construction of optimum distance flag codes

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2021-08
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Elsevier
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Abstract
Flag codes are multishot network codes consisting of sequences of nested subspaces (flags) of a vector space Fnq , where q is a prime power and Fq, the finite field of size q. In this paper we study the construction on F2kq 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 F2kq 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 F2kq that strongly depends on the characteristic of the field.
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Network coding, Spreads, Subspace codes, Orbit codes, Flag codes, General linear group
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Alonso-González, C., Navarro-Pérez, M. Á., & Soler-Escrivà, X. (2021). An orbital construction of optimum distance flag codes. Finite Fields and Their Applications, 73, 101861.