Content deleted Content added
Line 5:
Locally Recoverable Codes are a family of error correction codes that were introduced first by D. S. Papailiopoulos and A. G. Dimakis and have been widely studied in Information theory due to their applications related to Distributive and Cloud Storage Systems.
==Definition
Let <math>C</math> be a <math>[n, k, d]_{q}</math> linear code. For <math>i \in \{1, \ldots, n\}</math>, let us denote by <math>r_{i}</math> the minimum number of other coordinates we have to look at to recover an erasure in coordinate <math>i</math>. The number <math>r_{i}</math> is said to be the ''locality of the <math>i</math>-th coordinate'' of the code. The ''locality'' of the code is defined as <div style="text-align: center;"><math>r = max\{r_{i}|i \in \{1, \ldots, n\}\}</math></div>
Line 13:
Let <math>C</math> be an <math>[n, k, d]_{q}</math>-locally recoverable code. Then a deleted component can be recovered linearly, i.e. for every <math>i \in \{1, \ldots, n\}</math>, the space of linear equations of the code contains elements of the form <math> x_{i} = f(x_{i}, \ldots, x_{i_{r}})</math>, where <math>i_{j} \neq i</math>.
==Optimal Locally Recoverable Codes==
| |||