Add to ORKGWe consider the Grassmann graph of $k$-dimensional subspaces of an $n$-dimensional vector space over the $q$-element field and its subgraph $\Gamma(n,k)_q$ formed by non-degenerate linear $[n,k]_q$ codes. We assume that $1<k<n-1$. It is well-known that every automorphism of the Grassmann graph is induced by a semilinear automorphism of the corresponding vector space or a semilinear isomorphism to the dual vector space; the second possibility is realized only if $n=2k$. Our results are the following: if $q\ge 3$ or $k\ne 2$, then every isomorphism of $\Gamma(n,k)_{q}$ to a subgraph of the Grassmann graph can be uniquely extended to an automorphism of the Grassmann graph; in the case when $q=k=2$, there are subgraphs of the Grassmann graph is...
AbstractIn this paper we continue the investigation of a family of linear block codes based on the g...
Abstract. We discuss the problem of determining the complete weight hier-archy of linear error corre...
We discuss the problem of determining the complete weight hierarchy of linear error correcting codes...
We use a theorem of Chow (1949) on line-preserving bijections of Grassmannians to determine the auto...
Two mappings in a finite field, the Frobenius mapping and the cyclic shift mapping, are applied on l...
A linear [n, k]-code C is a k-dimensional subspace of V (n, q), where V (n, q) denotes the n-dimensi...
AbstractPerfect codes and optimal anticodes in the Grassman graph Gq(n, k) are examined. It is shown...
AbstractWe prove that the proportion of d-dimensional subspaces of an n-dimensional vector space ove...
We consider the question of determining the maximum number of points on sections of Grassmannians ov...
A linear [n, k] code of length n and dimension k over Fq = GF (q) is a k-dimensional vector subspace...
In this article, we introduce and characterize linear dependence graph Γ(V) of a finite dimensional ...
AbstractIf G is a graph and k is a field with char(K) ≠ 2 then the Grassmann algebra K(G) is the alg...
A linear [n, k]-code C is a k-dimensional subspace of V (n, q), where V (n, q) denotes the n-dimensi...
AbstractWe consider the question of determining the maximum number of points on sections of Grassman...
AbstractWe prove that the automorphism group of Generalized Reed-Muller codes is the general linear ...
AbstractIn this paper we continue the investigation of a family of linear block codes based on the g...
Abstract. We discuss the problem of determining the complete weight hier-archy of linear error corre...
We discuss the problem of determining the complete weight hierarchy of linear error correcting codes...
We use a theorem of Chow (1949) on line-preserving bijections of Grassmannians to determine the auto...
Two mappings in a finite field, the Frobenius mapping and the cyclic shift mapping, are applied on l...
A linear [n, k]-code C is a k-dimensional subspace of V (n, q), where V (n, q) denotes the n-dimensi...
AbstractPerfect codes and optimal anticodes in the Grassman graph Gq(n, k) are examined. It is shown...
AbstractWe prove that the proportion of d-dimensional subspaces of an n-dimensional vector space ove...
We consider the question of determining the maximum number of points on sections of Grassmannians ov...
A linear [n, k] code of length n and dimension k over Fq = GF (q) is a k-dimensional vector subspace...
In this article, we introduce and characterize linear dependence graph Γ(V) of a finite dimensional ...
AbstractIf G is a graph and k is a field with char(K) ≠ 2 then the Grassmann algebra K(G) is the alg...
A linear [n, k]-code C is a k-dimensional subspace of V (n, q), where V (n, q) denotes the n-dimensi...
AbstractWe consider the question of determining the maximum number of points on sections of Grassman...
AbstractWe prove that the automorphism group of Generalized Reed-Muller codes is the general linear ...
AbstractIn this paper we continue the investigation of a family of linear block codes based on the g...
Abstract. We discuss the problem of determining the complete weight hier-archy of linear error corre...
We discuss the problem of determining the complete weight hierarchy of linear error correcting codes...