Cyclic Self-Dual Codes(*)

N. J. A. Sloane 
Mathematics and Statistics Research Center 
Bell Labs, Murray Hill, N.J. 07974, USA  

and 

J. G. Thompson 
Department of Pure Mathematics and Mathematical Statistics 
University of Cambridge, Cambridge, CB2 1SB, ENGLAND  [+.2in]


Dedicated to Jessie MacWilliams in honor of her retirement from Bell Labs  


(*) A slightly different version of this paper appeared in
IEEE Trans. Information Theory, {bf 29 (1983), 364--366. 


ABSTRACT 

It is shown that if the automorphism
group of a binary self-dual code satisfies
a certain condition then the code contains
words of weight congruent to 2 modulo 4.
In particular, no cyclic binary
self-dual code can have all its weights divisible by 4.
The number of cyclic binary self-dual codes of
length n is determined, and the shortest
nontrivial code in this class is shown to
have length 14.


For the full paper, see:
http://www.research.att.com/~njas/doc/cyclic.pdf
or
http://www.research.att.com/~njas/doc/cyclic.ps