Searching for Minimum Storage Regenerating Codes
Daniel Cullina, Alexandros G. Dimakis, Tracey Ho · 2009
I would like to thank my thesis advisor, Professor Tracey Ho for introducing me to this topic and guiding me throughout the year. I would also like to thank Dr. Georgios Dimakis for helping me to understand his results regarding the problem and for sending me in fruitful directions. Special thanks to Sherwin Doroudi for his help during a variety of discussions throughout the year, to Mason Smith for his help with linear algebra, and to Shengbo Xu for his help during the writing process. Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We search for examples of Minimum Storage Regenerating Codes. To exhaustively search the space of potential codes, we reduce the potential search space in several ways. We impose an additional symmetry condition on codes that we consider. We specify codes in a simple alternative way, using additional recovered coefficients rather than transmission coefficients. We place codes into equivalence classes to avoid redundant checking. We find MSR codes for the parameters n = 5 and k = 3 in various fields. We demonstrate that it is possible