The paper focuses on binary array codes, which are widely used in storage systems to provide data redundancy and reliability. It introduces two new classes of binary array codes, V-ETBR and V-ESIP codes, which are derived from codes over a special polynomial ring F2[x]/⟨Pp−1
i=0 xiτ⟩, where p is an odd number and τ is a power of two.
The key highlights are:
The paper establishes the connections between the proposed variant codes and their counterparts over the polynomial ring, enabling the construction of binary MDS array codes with significantly more data columns compared to previous designs.
Explicit constructions for V-ETBR and V-ESIP MDS array codes are provided, based on Vandermonde and Cauchy matrices. These constructions allow for any number of parity columns and have a more flexible row size.
Fast syndrome computations are proposed for the Vandermonde-based V-ETBR and V-ESIP MDS array codes, meeting the lowest known asymptotic computational complexity among MDS codes.
The variant codes are based on simple binary parity-check matrices, making them attractive for practical implementation without requiring deep knowledge of algebra.
The paper also shows that the well-known generalized RDP codes are a special case of the proposed V-ESIP codes.
To Another Language
from source content
arxiv.org
Key Insights Distilled From
by Leilei Yu,Yu... at arxiv.org 04-02-2024
https://arxiv.org/pdf/2310.08271.pdfDeeper Inquiries