The Hamming distance of an array of storage devices is increased by
generating a parity check matrix based on column equations that are
formed using an orthogonal parity code and includes a higher-order
multiplier that changes each column. The higher order multiplier is
selected to generate a finite basic field of a predetermined number of
elements. The array has M rows and N columns, such that M is greater than
or equal to three and N is greater than or equal to three. Row 1 through
row M-2 of the array each have n p data storage devices and p parity
storage devices. Row M-1 of the array has n-(p+1) data storage devices
and (p+1) parity storage devices. Lastly, row M of the array has N parity
storage devices.