An algebraic approach for decoding spread codes

@article{Gorla2012AnAA,
  title={An algebraic approach for decoding spread codes},
  author={Elisa Gorla and Felice Manganiello and Joachim Rosenthal},
  journal={Adv. Math. Commun.},
  year={2012},
  volume={6},
  pages={443-466}
}
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size $k\times n$ with entries in a finite field $\mathbb F_q$. Spread codes are a family of optimal codes with maximal minimum distance. We give a minimum-distance decoding algorithm which requires $\mathcal{O}((n-k)k^3)$ operations over an extension field $\mathbb F_{q^k}$. Our algorithm is more efficient than the previous… 
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