An algorithm for augmenting a binary linear code is presented. The input to the code augmenting algorithm is (n,k,d) code C and the output is an (n,k*,d) augmented code C (k* k) satisfying C C and the Gilbert bound. The algorithm can be considered as an efficient implementation of the proof of Gilbert bound; for a given binary linear code C, the algorithm first finds a coset leader with the largest weight. If the weight of the coset leader is greater than or equal to the minimum distance of C, the coset leader is included to the basis of C.

It is shown that most of the binary images of generalized algebraic-geometric codes meet the Varshamov-Gilbert bound from the viewpoint of the average binary weight enumerator.

Asymptotic bounds are considered for unidirectional byte error-correcting codes. Upper bounds are developed from the concepts of the Singleton, Plotkin, and Hamming bounds. Lower bounds are also derived from a combination of the generalized concatenated code construction and the Varshamov-Gilbert bound. As the result, we find that there exist codes of low rate better than those on the basis of Hamming distance with respect to unidirectional byte error-correction.