1,145 research outputs found
Cyclic LRC Codes and their Subfield Subcodes
We consider linear cyclic codes with the locality property, or locally
recoverable codes (LRC codes). A family of LRC codes that generalizes the
classical construction of Reed-Solomon codes was constructed in a recent paper
by I. Tamo and A. Barg (IEEE Transactions on Information Theory, no. 8, 2014;
arXiv:1311.3284). In this paper we focus on the optimal cyclic codes that arise
from the general construction. We give a characterization of these codes in
terms of their zeros, and observe that there are many equivalent ways of
constructing optimal cyclic LRC codes over a given field. We also study
subfield subcodes of cyclic LRC codes (BCH-like LRC codes) and establish
several results about their locality and minimum distance.Comment: Submitted for publicatio
A family of optimal locally recoverable codes
A code over a finite alphabet is called locally recoverable (LRC) if every
symbol in the encoding is a function of a small number (at most ) other
symbols. We present a family of LRC codes that attain the maximum possible
value of the distance for a given locality parameter and code cardinality. The
codewords are obtained as evaluations of specially constructed polynomials over
a finite field, and reduce to a Reed-Solomon code if the locality parameter
is set to be equal to the code dimension. The size of the code alphabet for
most parameters is only slightly greater than the code length. The recovery
procedure is performed by polynomial interpolation over points. We also
construct codes with several disjoint recovering sets for every symbol. This
construction enables the system to conduct several independent and simultaneous
recovery processes of a specific symbol by accessing different parts of the
codeword. This property enables high availability of frequently accessed data
("hot data").Comment: Minor changes. This is the final published version of the pape
Asymptotic construction of locally repairable codes with multiple recovering sets
Locally repairable codes have been extensively investigated due to practical
applications in distributed and cloud storage systems in recent years. However,
not much work on asymptotic behavior of locally repairable codes has been done.
In particular, there is few result on constructive lower bound of asymptotic
behavior of locally repairable codes with multiple recovering sets. In this
paper, we construct some families of asymptotically good locally repairable
codes with multiple recovering sets via automorphism groups of function fields
of the Garcia-Stichtenoth towers. The main advantage of our construction is to
allow more flexibility of localities
- …