scholarly journals Generalized LMRD Code Bounds for Constant Dimension Codes

2020 ◽  
Vol 24 (10) ◽  
pp. 2100-2103
Author(s):  
Sascha Kurz
Keyword(s):  
Constant Dimension ◽  
Constant Dimension Codes

scholarly journals Consistent Flag Codes

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2234
Author(s):  
Clementa Alonso-González ◽  
Miguel Ángel Navarro-Pérez
Keyword(s):  
Finite Field ◽  
Consistency Condition ◽  
Decoding Algorithm ◽  
Constant Dimension ◽  
Constant Dimension Codes

In this paper we study flag codes on Fqn, being Fq 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.

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