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Binary block codes from Euclidean embeddings and random hyperplane tessellations

In this paper we use Euclidean embeddings and random hyperplane tessellations to construct binary block codes. The construction proceeds in two stages. First, an auxiliary ternary code is chosen which consists of vectors in the union of coordinate subspaces. The subspaces are selected so that any two vectors of different support have a sufficiently large distance. In addition, any two ternary vectors from the auxiliary codebook that have common support are at a guaranteed minimum distance. In the second stage, the auxiliary ternary code is converted to a binary code by an additional random hyperplane tessellation.