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Constructing large cyclic subspace codes using Sidon spaces
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AI
DOI：10.1007/s12190-025-02703-w.png)
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Abstract
En 中文
Sidon spaces serve as an important tool for investigating the properties of Fq-subspace multiplication and have been effectively used to construct large cyclic subspace codes in recent years. In this paper, we establish two distinct constructions of large cyclic subspace code utilizing Sidon spaces. By employing Sidon spaces with dimension k + 1, we obtain several large cyclic subspace codes with optimal minimum distance 2k. Notably, we establish that when n = 7k, the cyclic subspace codes in G(q)(7k, k + 1) have more codewords than previous works. Additionally, let n, k, l be positive integers satisfying kl|n and gcd(k, l) = 1. We explore Sidon spaces of dimension k + l to discover new cyclic subspace codes in G(q)(n, k + l). The parameters for cyclic subspace codes in Gq(n, k + l) are new and not covered by previous constructions, particularly when 5kl <= n < 7kl.
Keywords:
Sidon spaces
Large cyclic subspace codes
Minimum distance
Journal
J
IF:
2.7
Papers:
169
Citations:
0