An $[n,k]$ code is said to be a locally recoverable code with sequential recovery from t erasures, if for any set of $s leq t$ erasures, there is an s-step sequential recovery process, in which at each step, a single erased symbol is recovered by accessing at most r other code symbols. 

In this paper, a tight upper bound on the rate of such a code, for any value of number of erasures t and any value $ r geq 3$, of the locality parameter is derived. This bound proves an earlier conjecture due to Song, Cai and Yuen. While the bound is valid irrespective of the field over which the code is defined, a matching construction of binary codes that are rate-optimal is also provided, again for any value of t and any value $r geq 3$.

The very last part of the talk will briefly discuss a recent result on the construction of a high-rate MSR code with low field size and sub-packetization level and $d<(n-1)$. This last part is joint with Birenjith Sasidharan and Myna Vajha.