By Topic

Automorphisms of Order 2p in Binary Self-Dual Extremal Codes of Length a Multiple of 24

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Borello, M. ; Dipt. di Mat. e Applicazioni, Univ. degli Studi di Milano Bicocca, Milan, Italy ; Willems, W.

Let C be a binary self-dual code with an automorphism g of order 2p, where p is an odd prime, such that gp is a fixed point free involution. If C is extremal of length a multiple of 24, all the involutions are fixed point free, except the Golay Code and eventually putative codes of length 120. Connecting module theoretical properties of a self-dual code C with coding theoretical ones of the subcode C(gp) which consists of the set of fixed points of gp, we prove that C is a projective F2g 〉-module if and only if a natural projection of C(gp) is a self-dual code. We then discuss easy-to-handle criteria to decide if C is projective or not. As an application, we consider in the last part extremal self-dual codes of length 120, proving that their automorphism group does not contain elements of order 38 and 58.

Published in:

Information Theory, IEEE Transactions on  (Volume:59 ,  Issue: 6 )