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An optimal binary linear functional-repair storage code with efficient repair related to PG(2,8).

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Title: An optimal binary linear functional-repair storage code with efficient repair related to PG(2,8).
Authors: Hollmann, Henk D. L., Ke, Junming, Riet, Ago-Erik
Source: Designs, Codes & Cryptography; Nov2025, Vol. 93 Issue 11, p4721-4755, 35p
Subject Terms: PROJECTIVE geometry, LINEAR codes, ERROR-correcting codes, INFORMATION theory, APPLIED sciences
Abstract: 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. [ABSTRACT FROM AUTHOR]
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Abstract: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. [ABSTRACT FROM AUTHOR]
ISSN:09251022
DOI:10.1007/s10623-025-01682-0