OFFSET
1,8
COMMENTS
Fripertinger and Kerber (1995) mention that Slepian (1960) gave a generating function scheme for computing R_{n,k,2} = T(n,k), but it is not always correct. In Theorem 3.1, they give a corrected formula, but it seems too difficult to implement it in Sage. They do provide, however, a SYMMETRICA program for its computation (see the links). - Petros Hadjicostas, Oct 07 2019
LINKS
Discrete algorithms at the University of Bayreuth, Symmetrica.
Harald Fripertinger, Isometry Classes of Codes.
Harald Fripertinger, Rnk2: Number of the isometry classes of all binary indecomposable (n,k)-codes without zero columns. [This is a rectangular array, denoted by R_{nk2}, whose lower triangle (starting at n = 2) contains the current array T(n,k). The element R_{n=1,k=1,2} = 1 does not appear in the current array T(n,k).]
Harald Fripertinger, Enumeration of isometry-classes of linear (n,k)-codes over GF(q) in SYMMETRICA, Bayreuther Mathematische Schriften 49 (1999), 215-223. [For a SYMMETRICA program for the calculation of R_{nk2} = T(n,k), see pp. 219-220.]
H. Fripertinger and A. Kerber, Isometry classes of indecomposable linear codes, preprint, 1995. [We have T(n,k) = R_{nk2}; 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 T(n,k) = R_{nk2}; see p. 197.]
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.
EXAMPLE
Triangle T(n,k) (with rows n >= 2 and columns k >= 1) begins as follows:
1;
1, 1;
1, 1, 1;
1, 2, 2, 1;
1, 3, 5, 3, 1;
1, 4, 10, 10, 4, 1;
1, 5, 18, 28, 18, 5, 1;
1, 7, 31, 71, 71, 31, 7, 1;
1, 8, 51, 165, 250, 165, 51, 8, 1;
...
CROSSREFS
KEYWORD
tabl,nonn
AUTHOR
EXTENSIONS
More terms from Petros Hadjicostas, Oct 07 2019
STATUS
approved