An algebraic approach for decoding spread codes

We present a family of constant–dimension codes for random linear network codingcalled 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 matrixof an irreducible polynomial. We give a minimum distance decoding algorithm that isparticularly efficient when the dimension of the codewords is small. The decoding algo-rithm takes advantage of the structure of the algebra and it uses an original result onminors of a matrix and the factorization of polynomials over finite fields.