A034357 Number of binary [ n,3 ] codes.

0, 0, 1, 4, 10, 22, 43, 77, 131, 213, 333, 507, 751, 1088, 1546, 2159, 2967, 4023, 5384, 7122, 9322, 12081, 15512, 19752, 24950, 31283, 38953, 48188, 59244, 72419, 88037, 106469, 128129, 153476, 183019, 217331, 257033

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Also, a(n) is the number of orbits of C_2^3 subgroups of C_2^n under automorphisms of C_2^n. Also, a(n) is the number of faithful representations of C_2^3 of dimension n up to equivalence by automorphisms of (C_2^3). - Andrew Rupinski, Jan 20 2011

Links

• H. Fripertinger, Isometry Classes of Codes.
• Harald Fripertinger, Wnk2: Number of the isometry classes of all binary (n,k)-codes. [See column k=3.]
• H. Fripertinger and A. Kerber, Isometry classes of indecomposable linear codes, preprint, 1995. [We have a(n) = W_{n,3,2}; see p. 4 of the preprint.]
• 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. [We have a(n) = W_{n,3,2}; see p. 197.]

Crossrefs

Cf. A034198, A034253, A034254.

Column k=3 of both A034356 and A076831 (which are the same except for column k=0).

First differences give A034344.

Formula

G.f.: (-x^15+2*x^14-x^13+x^12+x^9-x^7+x^4+x^3)/((1-x)^3*(1-x^2)*(1-x^3)^2*(1-x^4)*(1-x^7)).