MSR Codes With Linear Field Size and Smallest Sub-Packetization for Any Number of Helper Nodes
MSR Codes With Linear Field Size and Smallest Sub-Packetization for Any Number of Helper Nodes
An <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(n, k, \ell)$ </tex-math></inline-formula> array code has k information coordinates and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r = n - k$ </tex-math></inline-formula> parity coordinates, where each coordinate is a vector in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {F}_{q}^{\ell }$ </tex-math></inline-formula> for some finite field <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> …