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A034343
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Number of inequivalent binary linear codes of length n and any dimension k <= n containing no column of zeros.
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6
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1, 2, 4, 8, 16, 36, 80, 194, 506, 1449, 4631, 17106, 74820, 404283, 2815595, 26390082, 344330452, 6365590987, 167062019455, 6182453531508, 319847262335488, 22968149462624180, 2277881694784784852
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OFFSET
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1,2
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COMMENTS
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Also, (by taking duals) number of inequivalent binary linear codes of length n and any dimension k <= n containing no codewords of weight 1.
It follows from the theorem on page 64 of Schwarzenberger (1980), this is also the number of Bravais types of orthogonal lattices in dimension n. (End)
Also the number of loopless binary matroids on n points.
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REFERENCES
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R. L. E. Schwarzenberger, N-Dimensional Crystallography. Pitman, London, 1980, pages 64 and 65.
M. Wild, Enumeration of binary and ternary matroids and other applications of the Brylawski-Lucas Theorem, Preprint No. 1693, Tech. Hochschule Darmstadt, 1994
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LINKS
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Discrete algorithms at the University of Bayreuth, Symmetrica. [This package was used to compute T_{nk2} using the cycle index of PGL_k(2). Here a(n) = T_{nn2}.]
H. Fripertinger and A. Kerber, Isometry classes of indecomposable linear codes. In: G. Cohen, M. Giusti, T. Mora (eds), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 11th International Symposium, AAECC 1995, Lect. Notes Comp. Sci. 948 (1995), pp. 194-204. [The notation for A076832(n,k) is T_{nk2}. Here a(n) = A076832(n,k) = T_{nn2}.]
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FORMULA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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