New binary codes
Neil J.A. Sloane, Sane Umesh Reddy, Chin-Long Chen · IEEE Transactions on Information Theory · 1972
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)^{1/2}symbols, of which only one is a check symbol, and thate-error-correcting BCH codes may sometimes be extended by (block !ength)^{1/e}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 withd/n = \frac{1}{3}, the first three being the(24,2^12, 8)Golay code, a(48,2^15, 16)code, and a(96,2^18, 32)code. Most of the codes given have more codewords than any comparable code previously known to us.