This site is supported by donations to The OEIS Foundation.



"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A034415 Second term in extremal weight enumerator of doubly-even binary self-dual code of length 24n. 4
1, 2576, 535095, 18106704, 369844880, 6101289120, 90184804281, 1251098739072, 16681003659936, 216644275600560, 2763033644875595, 34784314216176096, 433742858109499536, 5369839142579042560 (list; graph; refs; listen; history; text; internal format)



The terms become negative at n=154 and so certainly by that point the extremal codes do not exist (see references).

Up to n = 250 the terms steadily increase in magnitude, but their sign changes from positive to negative at n = 154.


F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, see Theorem 13, p. 624.


N. J. A. Sloane, Table of n, a(n) for n = 0..250

C. L. Mallows and N. J. A. Sloane, An Upper Bound for Self-Dual Codes, Information and Control, 22 (1973), 188-200.

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (Abstract, pdf, ps).

N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).


At length 24, the weight enumerator (of the Golay code) is 1+759*x^8+2576*x^12+..., with leading coefficient 759 and second term 2576.


For Maple program see A034414.


Cf. A034414 (leading coefficient), A001380, A034597, A034598.

Sequence in context: A001294 A109026 A217183 * A201510 A235094 A171257

Adjacent sequences:  A034412 A034413 A034414 * A034416 A034417 A034418




N. J. A. Sloane.



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 19 23:35 EDT 2017. Contains 290821 sequences.