Expanded Blaum–Roth Codes With Efficient Encoding and Decoding Algorithms

An expansion of Blaum-Roth codes by incorporating a vertical parity on p×p arrays, where p is a prime number, is described. The vertical parity allows for the local recovery of a symbol within a column without invoking the remaining columns. Efficient encoding and erasure decoding procedures are presented, in particular, for the case of two column parities.