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Search: id:A076831
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| A076831 |
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Triangle T(n,k) read by rows giving number of inequivalent binary linear [n,k] codes (n >= 0, 0 <= k <= n). |
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+0
4
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| 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 6, 16, 22, 16, 6, 1, 1, 7, 23, 43, 43, 23, 7, 1, 1, 8, 32, 77, 106, 77, 32, 8, 1, 1, 9, 43, 131, 240, 240, 131, 43, 9, 1, 1, 10, 56, 213, 516, 705, 516, 213, 56, 10, 1, 1, 11, 71, 333, 1060, 1988, 1988
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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"The familiar appearance of the first few rows [...] provides a good example of the perils of too hasty extrapolation in mathematics." - Slepian.
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REFERENCES
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H. Fripertinger and A. Kerber, in AAECC-11, Lect. Notes Comp. Sci. 948 (1995), 194-204.
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
D. Slepian, Some further theory of group codes. Bell System Tech. J. 39 1960 1219-1252.
M. Wild, Enumeration of binary and ternary matroids and other applications of the Brylawski-Lucas Theorem, Preprint Nr. 1693, Tech. Hochschule Darmstadt, 1994
M. Wild, Consequences of the Brylawski-Lucas Theorem for binary matroids, European Journal of Combinatorics 17 (1996) 309-316.
M. Wild, The asymptotic number of inequivalent binary codes and nonisomorphic binary matroids, Finite Fields and their Applications 6 (2000) 192-202.
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LINKS
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H. Fripertinger, Isometry Classes of Codes
Index entries for sequences related to binary linear codes
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EXAMPLE
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1; 1,1; 1,2,1; 1,3,3,1; 1,4,6,4,1; 1,5,10,10,5; 1,1,6,16,22,16,6,1; ...
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CROSSREFS
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Cf. A022166, A006116, A076766 (row sums). A034356 gives same table but with k=0 column omitted.
Sequence in context: A108086 A130595 A108363 this_sequence A119724 A162424 A008571
Adjacent sequences: A076828 A076829 A076830 this_sequence A076832 A076833 A076834
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KEYWORD
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nonn,tabl,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 21 2002
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