2022•arXiv (Cornell University)Open access

The graphs of non-degenerate linear codes

Mark Pankov

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Abstract

We consider the Grassmann graph of $k$-dimensional subspaces of an $n$-dimensional vector space over the $q$-element field and its subgraph $Γ(n,k)_q$ formed by non-degenerate linear $[n,k]_q$ codes. We assume that $1

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We consider the Grassmann graph of $k$-dimensional subspaces of an $n$-dimensional vector space over the $q$-element field and its subgraph $Γ(n,k)_q$ formed by non-degenerate linear $[n,k]_q$ codes. We assume that $1

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Available abstract

We consider the Grassmann graph of $k$-dimensional subspaces of an $n$-dimensional vector space over the $q$-element field and its subgraph $Γ(n,k)_q$ formed by non-degenerate linear $[n,k]_q$ codes. We assume that $1

Key concepts: Mathematics, Combinatorics, Automorphism, Linear subspace, Vector space, Exterior algebra, Grassmannian, Dual space

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