Locality and Availability of Array Codes Constructed From Subspaces

We study array codes which are based on subspaces of a linear space over a finite field, using spreads, <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-Steiner systems, and subspace transversal designs. We present several constructions of such codes which are <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>-analogs of some known block codes, such as the Hamming and simplex codes. We examine the locality and availability of the constructed codes. In particular, we distinguish between two types of locality and availability: node versus symbol. The resulting codes have distinct symbol/node locality/availability, allowing a more efficient repair process for a single symbol stored in a storage node of a distributed storage system, compared with the repair process for the whole node.

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