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   https://doi.org/10.1007/s10623-024-01456-0  

   Matthews, Gretchen_L; Morrison, Travis; Murphy, Aidan_W (July 2024, Designs, Codes and Cryptography)

   Abstract In this paper, we introduce curve-lifted codes over fields of arbitrary characteristic, inspired by Hermitian-lifted codes over$$\mathbb {F}_{2^r}$$ $F_{2^r}$. These codes are designed for locality and availability, and their particular parameters depend on the choice of curve and its properties. Due to the construction, the numbers of rational points of intersection between curves and lines play a key role. To demonstrate that and generate new families of locally recoverable codes (LRCs) with high availabilty, we focus on norm-trace-lifted codes. 

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2. Local List Recovery of High-Rate Tensor Codes & Applications

   https://doi.org/10.1109/FOCS.2017.27  

   Hemenway, Brett; Ron-Zewi, Noga; Wootters, Mary (October 2017, 58th Annual IEEE Symposium on Foundations of Computer Science)
3. Dual-Code Bounds on Multiple Concurrent (Local) Data Recovery

   https://doi.org/10.1109/ISIT50566.2022.9834616  

   Alfarano, Gianira N.; Ravagnani, Alberto; Soljanin, Emina (June 2022, 2022 IEEE International Symposium on Information Theory (ISIT))
4. Local List Recovery of High-Rate Tensor Codes and Applications

   https://doi.org/10.1137/17M116149X  

   Hemenway, Brett; Ron-Zewi, Noga; Wootters, Mary (January 2020, SIAM Journal on Computing)

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5. Global optimality of local search for low rank matrix recovery

   Bhojanapalli, Srinadh; Neyshabur, Behnam; Srebro, Nathan (May 2016, arXiv.org)

   We show that there are no spurious local minima in the non-convex factorized parametrization of low-rank matrix recovery from incoherent linear measurements. With noisy measurements we show all local minima are very close to a global optimum. Together with a curvature bound at saddle points, this yields a polynomial time global convergence guarantee for stochastic gradient descent from random initialization. 

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