Algebraic List-Decoding of Subspace Codes

Subspace codes are collections of subspaces of a cer- tain ambient vector space over a finite field. Koetter and Kschi- schang introduced subspace codes in order to correct errors and erasures in noncoherent (random) linear network coding. They have also studied a remarkable family of subspace codes obtained by evaluating certain linearized polynomials. The Koetter–Kschi- schang subspace codes are widely regarded as the counterpart of Reed–Solomon

codes in the domain of network error-correction. Koetter and Kschischang have furthermore devised an algebraic decoding algorithm for these codes, analogous to the Berlekamp– Welch decoding algorithm for Reed–Solomon codes.