Consistent Flag Codes

Clementa Alonso-González and Miguel Ángel Navarro-Pérez
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Clementa Alonso-González: Department of Mathematics, University of Alicante, San Vicente del Raspeig, Ap. Correos 99, E-03080 Alicante, Spain
Miguel Ángel Navarro-Pérez: Department of Mathematics, University of Alicante, San Vicente del Raspeig, Ap. Correos 99, E-03080 Alicante, Spain

Mathematics, 2020, vol. 8, issue 12, 1-19

Abstract: In this paper we study flag codes on F q n , being F q the finite field with q elements. Special attention is given 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 consistent 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 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 consistent flag codes that fully exploits the consistency condition.

Keywords: network coding; flag codes; constant dimension codes; equidistant codes; sunflowers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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