The set of all subspaces of F is denoted by ℙ(n). The subspace distance d(X, Y) = dim(X)+dim(Y)−2 dim(X∩Y) defined on ℙ(n) turns it into a natural coding space for error correction in random network coding. A subset of ℙ(n) is called a code and the subspaces that belong to the code are called codewords. Motivated by classical coding theory, a linear coding structure can be imposed on a subset of ℙ(n). Braun, Etzion and Vardy conjectured that the largest cardinality of a linear code, that contains F, is 2. In this paper, we prove this conjecture and characterize the maximal linear codes that contain F.
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