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A034358
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Number of binary [ n,4 ] codes.
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4
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0, 0, 0, 1, 5, 16, 43, 106, 240, 516, 1060, 2108, 4064, 7641, 14036, 25253, 44560, 77245, 131658, 220883, 365027, 594674, 955649, 1515908, 2374875, 3676632, 5627587, 8520689, 12767557, 18941641, 27834607, 40530902, 58503994, 83741461, 118904892, 167534794, 234309554, 325373538, 448747606
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OFFSET
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1,5
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LINKS
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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. [Here a(n) = W_{n,4,2}; see p. 197.]
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PROG
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(Sage) # Fripertinger's method to find the g.f. of column k >= 2 of A076831 or A034356 (for small k):
def A076831col(k, length):
G1 = PSL(k, GF(2))
G2 = PSL(k-1, GF(2))
D1 = G1.cycle_index()
D2 = G2.cycle_index()
f1 = sum(i[1]*prod(1/(1-x^j) for j in i[0]) for i in D1)
f2 = sum(i[1]*prod(1/(1-x^j) for j in i[0]) for i in D2)
f = (f1 - f2)/(1-x)
return f.taylor(x, 0, length).list()
# For instance the Taylor expansion for column k = 4 (this sequence) gives
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CROSSREFS
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Column k=4 of both A034356 and A076831 (which are the same except for column k=0).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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