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- W2159896754 abstract "Constant-weight codes play an important role in coding theory. The problem of determining the sizes for optimal quaternary constant-weight codes with length <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$n$</tex></formula> , weight 4, and minimum Hamming distance 5 ( <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex Notation=TeX>$(n,5,4)_{4}$</tex></formula> codes) has been investigated in several papers. Although some constructions and several infinite families for such codes with length <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$nequiv 0,1pmod4$</tex></formula> have been given, the problem is still far from complete. In this paper, we determine the size of an optimal <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex Notation=TeX>$(n,5,4)_{4}$</tex></formula> code for each integer <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex Notation=TeX>$ngeq 4$</tex></formula> leaving 55 lengths unsolved. Especially, for length <formula formulatype=inline xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex Notation=TeX>$nequiv 0,1pmod 4$</tex></formula> , the existence problem of the equivalent combinatorial object, namely the generalized Steiner system, is solved leaving only seven values undetermined." @default.
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- W2159896754 date "2013-03-01" @default.
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- W2159896754 title "Optimal Quaternary Constant-Weight Codes With Weight Four and Distance Five" @default.
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