New binary codes

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.