This paper presents a coding theory framework for random linear network coding in a noncoherent model where neither transmitter nor receiver has knowledge of the channel characteristics. The key idea is to model information transmission as the injection of a basis for a vector space V and the collection of a basis for a vector space U by the receiver. A metric on the projective geometry of the packet space is introduced, and it is shown that a minimum distance decoder achieves correct decoding if the dimension of the space V ∩ U is sufficiently large. The paper provides sphere-packing and sphere-covering bounds, as well as a generalization of the Singleton bound, for codes in this context. A Reed-Solomon-like code construction, related to Gabidulin's maximum rank-distance codes, is described, along with a Sudan-style "list-1" minimum distance decoding algorithm. The paper also discusses the connection between constant-dimension codes and rank-metric codes, and explores the implications of these codes for error and erasure correction in random linear network coding. The main result is the development of an efficient decoding algorithm for these codes, which asymptotically achieves the same rates as in the omniscient adversary model.This paper presents a coding theory framework for random linear network coding in a noncoherent model where neither transmitter nor receiver has knowledge of the channel characteristics. The key idea is to model information transmission as the injection of a basis for a vector space V and the collection of a basis for a vector space U by the receiver. A metric on the projective geometry of the packet space is introduced, and it is shown that a minimum distance decoder achieves correct decoding if the dimension of the space V ∩ U is sufficiently large. The paper provides sphere-packing and sphere-covering bounds, as well as a generalization of the Singleton bound, for codes in this context. A Reed-Solomon-like code construction, related to Gabidulin's maximum rank-distance codes, is described, along with a Sudan-style "list-1" minimum distance decoding algorithm. The paper also discusses the connection between constant-dimension codes and rank-metric codes, and explores the implications of these codes for error and erasure correction in random linear network coding. The main result is the development of an efficient decoding algorithm for these codes, which asymptotically achieves the same rates as in the omniscient adversary model.