1. A method comprising: receiving a digital communication signal; arranging said digital communication signal into an rxn matrix; linear transforming the rxn matrix of at least one n-dimensional input vector in a real or complex or a finite field by: storing in memory information about omitted rows, with respect to a selected row, in the matrix that are equivalent to one or more other rows in the matrix, including the selected row; omitting zero columns of said matrix and corresponding scalar components of the input vector; normalizing one or more columns of said matrix by multiplying the one or more columns by one or more lead element inverses of the one or more columns; generating a modified vector from groups in the normalized matrix; generating a modified matrix; and obtaining the output vector as indicative of said digital communication based at least in part on the omitted rows information.