相关论文: An even extremal lattice of rank 64

We extend the results of Ozeki on the configurations of extremal even unimodular lattices. Specifically, we show that if L is such a lattice of rank 56, 72, or 96, then L is generated by its minimal-norm vectors.

In this paper we propose a general ternary construction of lattices from three rows and ternary codes. Most laminated lattices and Kappa lattices in ${\bf R}^n$, $n\leq 24$ can be recovered from our tenary construction naturally. This…

For lengths $64$ and $66$, we construct extremal singly even self-dual codes with weight enumerators for which no extremal singly even self-dual codes were previously known to exist. We also construct new $40$ inequivalent extremal doubly…

We show that if L is an extremal even unimodular lattice of rank 40r with r=1,2,3 then L is generated by its vectors of norms 4r and 4r+2. Our result is an extension of Ozeki's result for the case r=1.

We construct a $40$-dimensional extremal Type II lattice not having any subsets consisting of $40$ orthogonal minimal vectors, and determine the automorphism group. This lattice gives an example different from the $16470$ lattices…

By constructing explicit examples, we show that the method of Quebbemann yields many isomorphism classes of extremal lattices of rank 64. Many of these examples have no non-trivial automorphisms.

We develop an algorithm computing the transcendental lattice and the Mordell--Weil group of an extremal elliptic surface. As an example, we compute the lattices of four exponentially large series of surfaces

We show that there is a unique extremal even unimodular lattice of dimension 48 which has an automorphism of order 5 of type 5-(8,16)-8. Since the three known extremal lattices do not admit such an automorphism, this provides a new example…

We review a lattice construction arising from quaternion algebras over number fields and use it to obtain some known extremal and densest lattices in dimensions 8 and 16. The benefit of using quaternion algebras over number fields is that…

We give a new proof of the fact that any finite quadratic module can be decomposed into indecomposable ones. For any indecomposable finite quadratic module, we construct a lattice, and a positive definite lattice, both of which are of the…

An $s$-extremal optimal unimodular lattice in dimension $52$ is constructed for the first time. This lattice is constructed from a certain self-dual $\mathbb{F}_5$-code by Construction A. In addition, as neighbors of the lattice, two more…

We show that, if L is an extremal Type II lattice of rank 40 or 80, then L is generated by its vectors of norm min(L)+2. This sharpens earlier results of Ozeki, and the second author and Abel, which showed that such lattices L are generated…

A Type II lattice of norm 8 in dimension 72 is obtained by Construction A applied to an extended Quadratic Residue code over Z8. Its automorphism group contains a subgroup isomorphic to PSL(2,71).

All extremal ternary codes of length 48 that have some automorphism of prime order $p\geq 5$ are equivalent to one of the two known codes, the Pless code or the extended quadratic residue code.

In this note, we demonstrate that every binary doubly even self-dual code of length $40$ can be realized as the residue code of some extremal Type II $\mathbb{Z}_4$-code. As a consequence, it is shown that there are at least $94356$…

In this work the construction of LRC codes given in [6] is completed, in the case of even characteristic. A general construction is presented, that enables us to obtain linear LRC codes of large length $n \approx q^4$, dimension and…

Extremal Type II $\mathbb{Z}_4$-codes are a class of self-dual $\mathbb{Z}_4$-codes with Euclidean weights divisible by eight and the largest possible minimum Euclidean weight for a given length. A small number of such codes is known for…

In this paper, we determine the dimensions of the residue codes of extremal Type II Z4-codes for lengths 32 and 40. We demonstrate that every binary doubly even self-dual code of length 32 can be realized as the residue code of some…

In this work, quadratic double and quadratic bordered double circulant constructions are applied to F_4 + uF_4 as well as F_4, as a result of which extremal binary self-dual codes of length 56 and 64 are obtained. The binary extension…

For some extremal (optimal) odd unimodular lattice $L$ in dimensions $12,16,20,28,32,36,40$ and $44$, we determine all integers $k$ such that $L$ contains a $k$-frame. This result yields the existence of an extremal Type I…