  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 x n) with entries in a finite field F_q. Spread codes are a
family of optimal codes with maximal minimum distance. We give a
minimum-distance decoding algorithm which requires O((n-k)k^3) operations over
an extension field F_{q^k}. Our algorithm is more efficient than the previous
ones in the literature, when the dimension k of the codewords is small with
respect to n. The decoding algorithm takes advantage of the algebraic structure
of the code, and it uses original results on minors of a matrix and on the
factorization of polynomials over finite fields.
