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==Optimal Locally Recoverable Codes==
'''Theorem 1.3''' Let <math>n = (r+1)s</math> and let <math>C</math> be an <math>[n, k, d]_{q}</math>-locally recoverable code having <math>s</math> disjoint locality sets of size <math>r+1</math>. Then, <div style="text-align: center;"><math>d \leq n - k - \left\lceil\frac{k}{r}\right\rceil + 2</math></div>
An <math>[n, k, d, r]_{q}</math>-LRC <math>C</math> is sai to be optimal if the minimum distance of <math>C</math> satisfies <div style="text-align: center;"><math>d = n - k - \left\lceil\frac{k}{r}\right\rceil + 2</math></div>
== Tamo-Barg Codes ==
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