1. A method of populating a plurality of columns for a check matrix that implements a distance d linear code, comprising: providing a set of vectors from which to populate said columns; applying to said set of vectors a filter operation that reduces said set by eliminating from said set all of said vectors that would, if used to populate said columns, prevent the check matrix from satisfying a column-wise linear independence requirement associated with check matrices of distance d linear codes and, thereafter, selecting from said set one of said vectors to populate one of said columns; and iteratively repeating said applying and thereafter selecting, until occurrence of one of population of all said columns, and reduction of said set to a total number of said vectors less than a total number of said columns that are currently unpopulated.