Binary codes from uniform subset graph G(n, ۴, i)

Let Ω be a set of cardinality n with n ≥ ۸, and let V = P۴(Ω) denote the family of all ۴-element subsets of Ω. For i = ۰, ۱, ۲, ۳, let G(n,۴,i) be the graph with vertex set V, where two vertices are adjacent precisely when their intersection has cardinality i. This graph is referred to as the uniform subset graph. We denote the adjacency matrix of G(n,۴,i) by Ai(n). In this work, we investigate the binary codes Ci(n) arising from the row space of Ai(n), determine their parameters, and establish the relationships between Ci(n) and Cj(n)⊥ for i,j ∈ {۰,۱,۲,۳}.

کلیدواژه ها:

Binary Codes ، design ، Graphs ، adjacency matrix