Classification of Distinct Maximal Flag Codes of a Prescriped Type and Related Results

Date

2023-8-31

Author

Karakaş, Zeynelabidin

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In this thesis, we aim to improve the current bounds for a certain type of code and not only find the number of distinct codes but also characterize them for some parameters. Flag codes have applications in network coding and their algebraic and combinatorial structures have been an active research area in recent years, see, for example, \cite{alonso,sascha}. Characterization of maximal flag codes of a given type and distance over a given ambient space is a very difficult problem. In this work, we completely solve this problem for small parameters with the help of MAGMA \cite{magma}. In particular, we find new maximal flag codes as well. For a given type and distance of a flag code, the number of distinct flag codes are determined exactly for some parameters, and we give bounds for arbitrary ones. The concept of set flag codes are given nicely and it is shown that some of the bounds of \cite{sascha} are not tight for all $q$.

Subject Keywords

Coding Theory, Graph Theory, Flag Codes, Permanents

URI

https://hdl.handle.net/11511/105942

Collections

Graduate School of Applied Mathematics, Thesis