In this paper constructions are given for combining two, three, or four codes to obtain new codes. The Andryanov-Saskovets construction is generalized. It is shown that the Preparata double-error-correcting codes may be extended by about (block length)

symbols, of which only one is a check symbol, and that

-error-correcting BCH codes may sometimes be extended by (block !ength)

symbols, of which only one is a check symbol. Several new families of linear and nonlinear double-error-correcting codes are obtained. Finally, an infinite family of linear codes is given with

, the first three being the

Golay code, a

code, and a

code. Most of the codes given have more codewords than any comparable code previously known to us.