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Search: id:A085960
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| A085960 |
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Size of the largest code of length 4 and minimum distance 3 over an alphabet of size n. This is usually denoted by A_{n}(4,3). |
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+0
1
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| 1, 2, 9, 16, 25, 34, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For n not 2 and not 6, a code C of size n^2 is given by two orthogonal Latin squares A and B of order n by C = {(i,j,A(i,j),B(i,j)): i,j in {1,...,n}}. Two orthogonal Latin squares of order n exist if and only if n is not 2 and not 6. See A055495.
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REFERENCES
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Raymond Hill, "A First Course in Coding Theory", Clarendon Press, Oxford, 1986 (see chapter 10, Theorem 10.16)
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FORMULA
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a(n) = 2 if n = 2, a(n) = 34 if n = 6, otherwise a(n) = n^2
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EXAMPLE
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a(2) = 2 since the code C={0000,1110} has minimum distance 3 over the alphabet {0,1} and there is no such code with more codewords.
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CROSSREFS
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Cf. A055495.
Sequence in context: A017005 A131189 A011193 this_sequence A051386 A003325 A101420
Adjacent sequences: A085957 A085958 A085959 this_sequence A085961 A085962 A085963
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KEYWORD
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easy,nonn
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AUTHOR
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W. Edwin Clark (eclark(AT)math.usf.edu), Aug 17 2003
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Feb 16 2005
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