OFFSET
1,5
LINKS
Harald Fripertinger, Isometry Classes of Codes.
Harald Fripertinger, Wnk2: Number of the isometry classes of all binary (n,k)-codes. [See column k=4.]
H. Fripertinger and A. Kerber, Isometry classes of indecomposable linear codes, preprint, 1995. [Here a(n) = W_{n,4,2}; 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. [Here a(n) = W_{n,4,2}; see p. 197.]
Petros Hadjicostas, Generating function for a(n).
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
David Slepian, Some further theory of group codes, Bell System Tech. J. 39(5) (1960), 1219-1252.
David Slepian, Some further theory of group codes, Bell System Tech. J. 39(5) (1960), 1219-1252.
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.
PROG
(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
print(A076831col(4, 30)) # Petros Hadjicostas, Oct 07 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Petros Hadjicostas, Oct 07 2019
STATUS
approved