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<p>Only a single example is known of a regenerating code with both small field size and efficient repair, and with parameters attaining a corner point of the achievable region determined by the cut-set bound, different from the MSR and MBR points. Here we present another such code, based on a vector space partition of a 9-dimensional binary space into 73 subspaces of dimension 3 that is strongly related to the projective plane PG(2,8); the coding spaces of the code consist of 72 of the subspaces in the partition. The new storage code comes with an efficient repair algorithm that can be described in terms of the underlying geometry. We provide complete descriptions of both the old and the new code, together with efficient repair methods. An extended abstract based on this work was presented at ISIT 2024.</p>

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An optimal binary linear functional-repair storage code with efficient repair related to \(\textrm{PG}(2,8)\)

  • 期刊论文

  • 发表日期：

    2025年7月28日

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  • Henk D. L. Hollmann,
  • Junming Ke,
  • Ago-Erik Riet

摘要

Only a single example is known of a regenerating code with both small field size and efficient repair, and with parameters attaining a corner point of the achievable region determined by the cut-set bound, different from the MSR and MBR points. Here we present another such code, based on a vector space partition of a 9-dimensional binary space into 73 subspaces of dimension 3 that is strongly related to the projective plane PG(2,8); the coding spaces of the code consist of 72 of the subspaces in the partition. The new storage code comes with an efficient repair algorithm that can be described in terms of the underlying geometry. We provide complete descriptions of both the old and the new code, together with efficient repair methods. An extended abstract based on this work was presented at ISIT 2024.