An algebraic approach for decoding spread codes

We present a family of constant–dimension codes for random linear network coding called spread codes. This is a family of optimal codes with maximum minimum distance. A spread code is constructed starting from the algebra defined by the companion matrix of an irreducible polynomial. We give a minimum distance decoding algorithm that is particularly efficient when the dimension of the codewords is small. The decoding algorithm takes advantage of the structure of the algebra and it uses an original result on minors of a matrix and the factorization of polynomials over finite fields.