Rack-Aware MSR Codes with Linear Field Size and Smaller Sub-Packetization for Tolerating Multiple Erasures

In an (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n, k, d</i>) rack-aware storage model, the system consists of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> nodes uniformly distributed across <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> successive racks, such that each rack contains <italic xmlns:mml="http://www.w3.org/1998/M