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- W2034885014 abstract "An interesting open question is whether a <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>(72, 36, 16)</tex> doubly even code <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>C</tex> exists. In [3] the odd prime numbers which can divide the order of the group of <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>C</tex> were determined and <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>23</tex> is the largest of these. Twenty-three is eliminated by reducing the problem to the consideration of <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>348</tex> codes, each of which is shown to have minimum weight <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>12</tex> or less. One of these codes, denoted by <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>C'</tex> , arises from the <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>(a + x, b + x, a + b + x)</tex> construction where <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>a</tex> and <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>b</tex> are in one quadratic residue code and <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>x</tex> is in the other. The weight distribution of <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>C'</tex> is given." @default.
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- W2034885014 date "1982-01-01" @default.
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- W2034885014 title "23 does not divide the order of the group of a (72,36,16) doubly even code (Corresp.)" @default.
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