Coherent Flag Codes

11/05/2020

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by   Clementa Alonso-González, et al.

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In this paper we study flag codes on 𝔽_q^n, being 𝔽_q the finite field with q elements, paying special attention to the connection between the parameters and properties of a flag code and the ones of a family of constant dimension codes naturally associated to it (the projected codes). More precisely, we focus on coherent flag codes, that is, flag codes whose distance and size are completely determined by their projected codes. We explore some aspects of this family of codes and present interesting examples of them by generalizing the concepts of equidistant and sunflower subspace code to the flag codes setting. Finally, we present a decoding algorithm for coherent flag codes that fully exploits the coherence condition.