The Binary Self-Dual Codes of Length Up To 32: A Revised Enumeration

J. H. Conway
Mathematics Department
Princeton University
Princeton, NJ 08540

V. Pless
Mathematics Department
University of Illinois at Chicago
Chicago, IL 60680

N. J. A. Sloane(*)
Mathematical Sciences Research Center
AT&T Bell Laboratories
Murray Hill, NJ 07974

(*) Present address:
Information Sciences Research
AT&T Shannon Lab
Florham Park, NJ 07932-0971


ABSTRACT

This paper presents a revised enumeration of the binary self-dual codes
of length up to 32 given in "On the enumeration of self-dual codes"
(by J. H. C. and V.P.) and "The children of the (32,16) doubly even codes" (by V.P.).
The list of eighty-five doubly-even self-dual codes of length 32 given
in the first paper is essentially correct, but several of their
descriptions need amending.  The principal change is that there are 731 
(not 664) inequivalent self-dual codes of length 30.  Furthermore
there are three (not two) [28,14,6] and thirteen (not eight)
[30,15,6] self-dual codes.  Some additional
information is provided about the self-dual codes of length less than 32.


For the full version see
http://www.research.att.com/~njas/doc/pless.pdf (pdf) or
http://www.research.att.com/~njas/doc/pless.ps (ps)
[note:
<a href="http://www.research.att.com/~njas/doc/plesstaba.ps"> Table A </a> and
<a href="http://www.research.att.com/~njas/doc/plesstabd.ps"> Table D </a>
are in separate files]



A different version of this paper appeared in J. Combinatorial Theory, Series A,
60 (1992), 183-195.