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New binary codes

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3 Author(s)

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 that e -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 with d/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.

Published in:

IEEE Transactions on Information Theory  (Volume:18 ,  Issue: 4 )