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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&#x2013;Kschi- schang subspace codes are widely regarded as the counterpart of Reed&#x2013;Solomon <?Pub _interword-space ?>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&#x2013; Welch decoding algorithm for Reed&#x2013;Solomon codes.

Algebraic List-Decoding of Subspace Codes