New Constructions of Sidon Spaces and Cyclic Subspace Codes

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  • LIU Xue-Mei
    College of Sciences, Civil Aviation University of China
  • SHI Tong
    College of Sciences, Civil Aviation University of China
  • NIU Min-Yao
    School of Sciences, Beijing University of Posts and Telecommunications
  • SHEN Lin-Zhi
    College of Sciences, Civil Aviation University of China
  • GAO You
    College of Science, Tianjin Key Lab for Advanced Signal Processing, Civil Aviation University of China

Abstract

<p>Sidon space is an important tool for constructing cyclic subspace codes. In this letter, we construct some Sidon spaces by using primitive elements and the roots of some irreducible polynomials over finite fields. Let q be a prime power, k, m, n be three positive integers and $\rho= \lceil \frac{m}{2k}\rceil-1$, $\theta= \lceil \frac{n}{2m}\rceil-1$. Based on these Sidon spaces and the union of some Sidon spaces, new cyclic subspace codes with size $\frac{3(q^{n}-1)}{q-1}$ and $\frac{\theta\rho q^{k}(q^{n}-1)}{q-1}$ are obtained. The size of these codes is lager compared to the known constructions from [14] and [10].</p>

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