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- W2115789360 abstract "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) <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>^{1/2}</tex> symbols, of which only one is a check symbol, and that <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>e</tex> -error-correcting BCH codes may sometimes be extended by (block !ength) <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>^{1/e}</tex> 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 <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>d/n = frac{1}{3}</tex> , the first three being the <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>(24,2^12, 8)</tex> Golay code, a <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>(48,2^15, 16)</tex> code, and a <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>(96,2^18, 32)</tex> code. Most of the codes given have more codewords than any comparable code previously known to us." @default.
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- W2115789360 date "1972-07-01" @default.
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- W2115789360 title "New binary codes" @default.
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- W2115789360 doi "https://doi.org/10.1109/tit.1972.1054833" @default.
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