A method of encoding generalized concatenated error-correcting codes includes providing a parity matrix {tilde over (H)}j of a j-th layer code and predefined syndrome {tilde over (s)} of length n−{tilde over (k)}j, where the first n-kl coordinates are zero, n is a length of a codeword c of a first layer BCH code Cl of dimension {tilde over (k)}j, codeword c satisfies {tilde over (H)}jc={tilde over (s)}, a first layer code includes only a BCH code, and each subsequent layer includes a Reed-Solomon (RS) stage followed by a BCH code; finding a square matrix R, of dimension (n−{tilde over (k)}j)(n−{tilde over (k)}j) such that Rj{tilde over (H)}j=(A|I), where A is an arbitrary matrix, Rj=(Qj|Tj), where Q has n−kl columns Tj and has k1−{tilde over (k)}j columns; finding a vector c−(a b) where a is a vector of length {tilde over (k)}j and b is a vector of length n−{tilde over (k)}j; and solving ( A | I ) ⁢ ( a b ) = ( Q j | T j ) ⁢ s ~ = T j ⁢ s ⁢ ⁢ where ⁢ ⁢ a = 0 ⁢ ⁢ and ⁢ ⁢ b = T j ⁢ s , where a=0 and b=Tjs, and codeword c is nonzero only on the last n−{tilde over (k)}j=n−kj bits.