New Constructions of Full Flag Codes Based on Partial Spreads

2025/06/18 by Xinran Li, Han, Xiang, Gang Wang +2
Biochemistry, Genetics and Molecular Biology · Computer Science · #Coding theory and cryptography #DNA and Biological Computing #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.2506.15127

openalex publication_date 2025/06/18 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

Flag codes are a class of multishot network codes comprising sequences of nested subspaces (flags) within the vector space \mathbbF_qⁿ, 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.

Citations

• Quasi-optimum distance flag codes
• Flag codes of maximum distance and constructions using Singer groups
• Cyclic Orbit Flag Codes
• An Orbital Construction of Optimum Distance Flag Codes
• Flag Codes from Planar Spreads in Network Coding
• The maximum size of a partial spread in a finite projective space
• Partial Spreads in Random Network Coding
• An Algebraic Approach for Decoding Spread Codes
• Coding for Errors and Erasures in Random Network Coding

Related

• Flag Codes from Planar Spreads in Network Coding
• Quasi-optimum distance flag codes
• Optimum Distance Flag Codes from Spreads via Perfect Matchings in Graphs
• A Combinatorial Approach to Flag Codes
• Motzkin numbers and flag codes