New family of single-error correcting codes

A construction is given that combines an
(n, M_1, d_1)
code with an
(n, M_2, d_2 = [\frac{1}{2}(d_1 + 1)])
code to form a
(2n, M_1 M_2, d_1)
code. This is used to construct a new family of nongroup single-error correcting codes of all lengths
n
from
2^m
to 3 ·
2^{m-1} - 1
, for every
m \geq 3
. These codes have more codewords than any group code of the same length and minimum distance. A number of other nongroup codes are also obtained. Examples of the new codes are (16,2560,3) and (16,36,7) codes, both having more codewords than any comparable group code.