Related papers: Some new results on the self-dual [120,60,24] code

A long-standing conjecture asserts that every finite non-abelian $p$-group has a non-inner automorphism of order $p$. In this paper, we settle the conjecture for a finite $p$-group ($p >2$) of nilpotency class $n$ with certain conditions.

In this paper, a virus optimization algorithm, which is one of the metaheuristic optimization technique, is employed for the first time to the problem of finding extremal binary self-dual codes. We present a number of generator matrices of…

$\operatorname{SL}(2,q)$-unitals are unitals of order $q$ admitting a regular action of $\operatorname{SL}(2,q)$ on the complement of some block. They can be obtained from affine $\operatorname{SL}(2,q)$-unitals via parallelisms. We compute…

In this paper, constructions of some double circulant self-dual codes by generalized cyclotomic classes of order two are presented. This technique is applied to [72, 36, 12] binary highest know self-dual codes to obtain self-dual codes over…

In this paper, we determine the automorphism group of the $p$-cones ($p\neq 2$) in dimension greater than two. In particular, we show that the automorphism group of those $p$-cones are the positive scalar multiples of the generalized…

Let $K$ be a field and $f:\mathbb{P}^N \to \mathbb{P}^N$ a morphism. There is a natural conjugation action on the space of such morphisms by elements of the projective linear group $\text{PGL}_{N+1}$. The group of automorphisms, or…

In this paper we study the existence of at least one non-inner automorphism of order p in a finite normally constrained p-group when p is an odd prime.

Additive codes over GF(9) that are self-dual with respect to the Hermitian trace inner product have a natural application in quantum information theory, where they correspond to ternary quantum error-correcting codes. However, these codes…

In this paper we study the existence of at least one non-inner automorphism of order p of a finite thin p-group, for any prime p.

Let $X$ be a complex projective variety. Suppose that the group of birational automorphisms of $X$ contains finite subgroups isomorphic to $(\mathbb{Z}/N\mathbb{Z})^r$ for $r$ fixed and $N$ arbitrarily large. We show that $r$ does not…

We obtain sharp lower and upper bounds for the number of maximal (under inclusion) independent sets in trees with fixed number of vertices and diameter. All extremal trees are described up to isomorphism.

We study upper bounds on the order of automorphisms of non-singular curves $X$ satisfying at least one of the following hypothesis: 1) $X$ is an $m$-sheeted covering of exactly one non-singular curve of genus $\gamma$, where $m$ is prime;…

Self-orthogonal codes are an important subclass of linear codes which have nice applications in quantum codes and lattices. It is known that a binary linear code is self-orthogonal if its every codeword has weight divisible by four, and a…

We argue that the existence of a modular differential equation implies that a certain vector vanishes in Zhu's C2 quotient space, and we check this assertion in numerous examples. If this connection is true in general, it would imply that…

We determine the structure of automorphism groups of finite graphs of bounded Hadwiger number. Our proof includes a structural analysis of finite edge-transitive graphs. In particular, we show that for connected, $K_{h+1}$-minor-free,…

If an outer (multilinear) commutator identity holds in a large subgroup of a group, then it holds also in a large characteristic subgroup. Similar assertions are valid for algebras and their ideals or subspaces. Varying the meaning of the…

We review the general formalism of duality rotations for $\cal N$-extended (super)conformal gauge multiplets of arbitrary (super)spin in four dimensions, with ${\cal N} \geq 0$. Self-dual models for a vector field (${\cal N}=0$) and for…

A rigid automorphism of a linking system is an automorphism which restricts to the identity on the Sylow subgroup. A rigid inner automorphism is conjugation by an element in the center of the Sylow subgroup. At odd primes, it is known that…

In this paper, we investigate the existence and asymptotic property of self-dual $2$-quasi negacyclic codes of length $2n$ over a finite field of cardinality $q$. When $n$ is odd, we show that the $q$-ary self-dual $2$-quasi negacyclic…

We show that every automorphism of a thick twin building interchanging the halves of the building maps some residue to an opposite one. Furthermore we show that no automorphism of a locally finite 2-spherical twin building of rank at least…