On some self-dual codes and unimodular lattices in dimension 48
نویسندگان
چکیده
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 selfdual [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. © 2005 Elsevier Ltd. All rights reserved.
منابع مشابه
Ternary Code Construction of Unimodular Lattices and Self-Dual Codes over <Subscript>6</Subscript>
We revisit the construction method of even unimodular lattices using ternary self-dual codes given by the third author (M. Ozeki, in Théorie des nombres, J.-M. De Koninck and C. Levesque (Eds.) (Quebec, PQ, 1987), de Gruyter, Berlin, 1989, pp. 772–784), in order to apply the method to odd unimodular lattices and give some extremal (even and odd) unimodular lattices explicitly. In passing we cor...
متن کاملSome extremal self-dual codes and unimodular lattices in dimension 40
In this paper, binary extremal singly even self-dual codes of length 40 and extremal odd unimodular lattices in dimension 40 are studied. We give a classification of extremal singly even self-dual codes of length 40. We also give a classification of extremal odd unimodular lattices in dimension 40 with shadows having 80 vectors of norm 2 through their relationships with extremal doubly even sel...
متن کاملSelf-Dual Codes over Z4 and Unimodular Lattices: A Survey
By using Construction A modulo 4 the following remarkable unimodular lattices have been constructed: the Gosset lattice E8, the Leech lattice, the 23 Niemeier lattices in dimension 24, the two extremal even unimodular lattices in dimension 32 with an automorphism of order 31, all the extremal unimodular lattices and the odd Leech lattice. In this survey, we review basic facts of life in the Z4 ...
متن کاملType II Self-Dual Codes over Finite Rings and Even Unimodular Lattices
In this paper, we investigate self-dual codes over finite rings, specifically the ring Z2m of integers modulo 2m . Type II codes over Z2m are introduced as self-dual codes with Euclidean weights which are a multiple of 2m+1. We describe a relationship between Type II codes and even unimodular lattices. This relationship provides much information on Type II codes. Double circulant Type II codes ...
متن کاملExtremal Self - Dual Codes over Z 6 , Z 8 and Z 10
In this paper, upper bounds on the minimum Euclidean weights of Type I codes over Z6 , and self-dual codes over Z8 and Z10 , are derived for modest lengths. The notion of extremality for Euclidean weights is also introduced. We construct new extremal self-dual codes over these rings. Most of these codes are obtained via the double circulant and quasitwisted constructions. New extremal odd unimo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 26 شماره
صفحات -
تاریخ انتشار 2005