منابع مشابه
On Locally Recoverable (LRC) Codes
We present simple constructions of optimal erasure-correcting LRC codes by exhibiting their parity-check matrices. When the number of local parities in a parity group plus the number of global parities is smaller than the size of the parity group, the constructed codes are optimal with a field of size at least the length of the code. We can reduce the size of the field to at least the size of t...
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We point some contributions to the construction of Locally Recoverable codes from algebraic curves recently presented by A. Barg, I. Tamo and S. Vladut, that can lead to improvements concerning the definition, the parameters and the local recovering of these codes.
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New stabilizer codes with parameters better than the ones available in the literature are provided in this work, in particular quantum codes with parameters [[127, 63,≥ 12]]2 and [[63, 45,≥ 6]]4 that are records. These codes are constructed with a new generalization of the Steane’s enlargement procedure and by considering orthogonal subfield-subcodes –with respect to the Euclidean and Hermitian...
متن کاملOn the distance of stabilizer quantum codes from J-affine variety codes
Self-orthogonal J-affine variety codes have been successfully used to obtain quantum stabilizer codes with excellent parameters. In a previous paper we gave formulae for the dimension of this family of quantum codes, but no bound for the minimum distance was given. In this work, we show how to derive quantum stabilizer codes with designed minimum distance from J-affine variety codes and their s...
متن کاملIntegrated interleaved codes as locally recoverable codes: properties and performance
Considerable interest has been paid in recent literature to codes combining local and global properties for erasure correction. Applications are in cloud type of implementations, in which fast recovery of a failed storage device is important, but additional protection is required in order to avoid data loss, and in RAID type of architectures, in which total device failures coexist with silent f...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2020
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2020.101661