A076766 Number of inequivalent binary linear codes of length n. Also the number of nonisomorphic binary matroids on an n-set.

1, 2, 4, 8, 16, 32, 68, 148, 342, 848, 2297, 6928, 24034, 98854, 503137, 3318732, 29708814, 374039266, 6739630253, 173801649708, 6356255181216, 326203517516704, 23294352980140884, 2301176047764925736, 313285408199180770635, 58638266023262502962716

Offset

0,2

References

M. Wild, Enumeration of binary and ternary matroids and other applications of the Brylawski-Lucas Theorem, Preprint Nr. 1693, Tech. Hochschule Darmstadt, 1994.

Links

Table of n, a(n) for n=0..25.

Jayant Apte and J. M. Walsh, Constrained Linear Representability of Polymatroids and Algorithms for Computing Achievability Proofs in Network Coding, arXiv preprint arXiv:1605.04598 [cs.IT], 2016-2017.

Suyoung Choi and Hanchul Park, Multiplication structure of the cohomology ring of real toric spaces, arXiv:1711.04983 [math.AT], 2017.

H. Fripertinger, Isometry Classes of Codes.

Dillon Mayhew and Gordon F. Royle, Matroids with nine elements, arXiv:math/0702316 [math.CO], 2007.

Dillon Mayhew and Gordon F. Royle, Matroids with nine elements, J. Combin. Theory Ser. B 98(2) (2008), 415-431.

James Oxley, What is a Matroid?.

Gordon Royle and Dillon Mayhew, 9-element matroids.

D. Slepian, On the number of symmetry types of Boolean functions of n variables, Canadian J. Math. 5, (1953), 185-193.

D. Slepian, A class of binary signaling alphabets, Bell System Tech. J. 35 (1956), 203-234.

D. Slepian, Some further theory of group codes, Bell System Tech. J. 39 1960 1219-1252. (Row sums of Table II.)

Marcel Wild, Consequences of the Brylawski-Lucas Theorem for binary matroids, European Journal of Combinatorics 17 (1996), 309-316.

Marcel Wild, The asymptotic number of inequivalent binary codes and nonisomorphic binary matroids, Finite Fields and their Applications 6 (2000), 192-202.

Marcel Wild, The asymptotic number of binary codes and binary matroids, SIAM J. Discrete Math. 19 (2005), 691-699. [This paper apparently corrects some errors in previous papers.]

Index entries for sequences related to binary linear codes

Example

a(2)=4 because there are four inequivalent linear binary 2-codes: {(0,0)}, {(0,0),(1,0)}, {(0,0),(1,1)}, {(0,0),(1,0),(0,1),(1,1)}. Observe that the codes {(0,0),(1,0)} and {(0,0),(0,1)} are equivalent because one arises from the other by a permutation of coordinates.

Crossrefs

Row sums of triangle A076831. Cf. A034328, A055545.

Sequence in context: A180208 A100139 A274860 * A344492 A359389 A275072

Adjacent sequences: A076763 A076764 A076765 * A076767 A076768 A076769

Keyword

nice,nonn

Author

Marcel Wild (mwild(AT)sun.ac.za), Nov 14 2002

Extensions

Edited by N. J. A. Sloane, Nov 01 2007, at the suggestion of Gordon Royle.

Status

approved