Multilinear algebra for minimum storage regenerating codes: a generalization of the product-matrix construction

An (n, k, d, α) -MSR (minimum storage regeneration) code is a set of n nodes used to store a file. For a file of total size kα, each node stores α symbols, any k nodes determine the file, and any d nodes can repair any other node by each sending out α/ (d- k+ 1) symbols. In this work, we express the product-matrix construction of (n, k, 2 (k- 1) , k- 1) -MSR codes in terms of symmetric algebras. We then generalize the product-matrix construction to (n,k,(k-1)tt-1,(k-1t-1))-MSR codes for general t⩾ 2 , while the t= 2 case recovers the product-matrix construction. Our codes’ sub-packetization level—α—is small and independent of n. It is less than L^2.8(d-k+1), where L is Alrabiah–Guruswami’s lower bound on α. Furthermore, it is less than other MSR codes’ α for a set of practical parameters. Finally, we discuss how our code repairs multiple failures at once.