cp's OEIS Frontend

A034357 Number of binary [ n,3 ] codes.

%I A034357 #23 Jul 08 2025 20:17:16
%S A034357 0,0,1,4,10,22,43,77,131,213,333,507,751,1088,1546,2159,2967,4023,
%T A034357 5384,7122,9322,12081,15512,19752,24950,31283,38953,48188,59244,72419,
%U A034357 88037,106469,128129,153476,183019,217331,257033
%N A034357 Number of binary [ n,3 ] codes.
%C A034357 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
%H A034357 H. Fripertinger, <a href="http://www.mathe2.uni-bayreuth.de/frib/codes/tables.html">Isometry Classes of Codes</a>.
%H A034357 Harald Fripertinger, <a href="http://www.mathe2.uni-bayreuth.de/frib/codes/tables_6.html">Wnk2: Number of the isometry classes of all binary (n,k)-codes</a>. [See column k=3.]
%H A034357 H. Fripertinger and A. Kerber, <a href="https://www.researchgate.net/publication/2550138_Isometry_Classes_of_Indecomposable_Linear_Codes">Isometry classes of indecomposable linear codes</a>, preprint, 1995. [We have a(n) = W_{n,3,2}; see p. 4 of the preprint.]
%H A034357 H. Fripertinger and A. Kerber, <a href="https://doi.org/10.1007/3-540-60114-7_15">Isometry classes of indecomposable linear codes</a>. 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.]
%F A034357 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)).
%Y A034357 Cf. A034198, A034253, A034254.
%Y A034357 Column k=3 of both A034356 and A076831 (which are the same except for column k=0).
%Y A034357 First differences give A034344.
%K A034357 nonn
%O A034357 1,4
%A A034357 _N. J. A. Sloane_