On some self-dual codes and unimodular lattices in dimension 48

Authors:
Masaaki Harada;Masaaki Kitazume;Akihiro Munemasa;Boris Venkov
Affiliations:
Department of Mathematical Sciences, Yamagata University, Yamagata 990-8560, Japan;Department of Mathematics and Informatics, Chiba University, Chiba 263-8522, Japan;Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan;Steklov Institute of Mathematics at St. Petersburg, St. Petersburg 191011, Russia
Venue:
European Journal of Combinatorics
Year:
2005

Citing 6
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Abstract

In this paper, binary extremal self-dual codes of length 48 and extremal unimodular lattices in dimension 48 are studied through their shadows and neighbors. We relate an extremal singly even self-dual [48, 24, 10] code whose shadow has minimum weight 4 to an extremal doubly even self-dual [48, 24, 12] code. It is also shown that an extremal odd unimodular lattice in dimension 48 whose shadow has minimum norm 2 relates to an extremal even unimodular lattice. Extremal singly even self-dual [48, 24, 10] codes with shadows of minimum weight 8 and extremal odd unimodular lattice in dimension 48 with shadows of minimum norm 4 are investigated.