An exponential lower bound on the sub-packetization of MSR codes
Omar Alrabiah, Venkatesan Guruswami · 2019
An (n,k,ℓ)-vector MDS code is a F-linear subspace of (Fℓ)n (for some field F) of dimension kℓ, such that any k (vector) symbols of the codeword suffice to determine the remaining r=n−k (vector) symbols. The length ℓ of each codeword symbol is called the Sub-Packetization of the code. Such a code is called minimum storage regenerating (MSR), if any single symbol of a codeword can be recovered by downloading ℓ/r field elements (which is known to be the least possible) from each of the other symbols.