Abstract. This talk builds on our recent research on the easy repair properties of simplex erasure codes for distributed storage (Kuijper, Lieb & Napp submitted 2025). Throughout the talk we focus on codes that allow for multi-erasure pattern decoding with low computational effort.To set the scene, we first give an overview of our earlier results for simplex block codes, mainly from Kuijper & Napp 2014. We then turn our attention to other block codes as well as convolutional erasure codes. We present codes of different rates that possess the easy repair property. The presented codes are all in some way related to simplex codes. We also formulate conditions under which the easy repairs can be performed in parallel, thus improving access speed of the distributed storage system.

Biography. Margreta Kuijper is a Professor at the Department of Electrical and Electronic Engineering of the University of Melbourne (Australia) where she has been employed since 1995. From 1992 to 1995 she was a postdoctoral fellow in the area of behavioral systems & control at the Mathematics Department ofthe University of Groningen, the Netherlands.  From 1988 to 1992 she worked at the Centrum Wiskunde & Informatica (CWI), Amsterdam, where she obtained her PhD degree in the area of behavioural systems & control in 1992. Her main research interests evolve around the interplay between systems theory and coding theory. Her research has addressed a diverse range of areas including behavioral system theory, polynomial matrix theory, convolutional coding, Reed-Solomon coding, distributed source coding, systems and codes over finite fields and rings, system cyber security, erasure coding for distributed storage and erasure coding for streaming applications.