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arXiv · 2506.15127

New Constructions of Full Flag Codes Based on Partial Spreads

Xiang Han·Xinran Li·Gang Wang
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Abstract

Flag codes are a class of multishot network codes comprising sequences of nested subspaces (flags) within the vector space $\mathbb{F}_q^n$, where $q$ is a prime power. In this paper, we propose a family of constructions for full flag codes based on partial spreads. The distances of this family include maximum distance (optimum distance flag codes), second-maximum distance (quasi-optimum distance flag codes), as well as other feasible values. The structure of these flag codes resembles that of a \textquotedblleft sandwich", consisting of one layer of companion matrix and two layers of partial spreads. Furthermore, we present an efficient decoding algorithm for these codes.

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Xiang Han, Xinran Li, Gang Wang. 2025-06-18. New Constructions of Full Flag Codes Based on Partial Spreads. https://arxiv.org/abs/2506.15127

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