منابع مشابه
MDS codes in Doob graphs
Аннотация The Doob graph D(m, n), where m > 0, is the direct product of m copies of The Shrikhande graph and n copies of the complete graph K 4 on 4 vertices. The Doob graph D(m, n) is a distance-regular graph with the same parameters as the Hamming graph H(2m + n, 4). In this paper we consider MDS codes in Doob graphs with code distance d ≥ 3. We prove that if 2m + n > 6 and 2 < d < 2m + n, th...
متن کاملPerfect codes in Doob graphs
We study 1-perfect codes in Doob graphsD(m,n). We show that such codes that are linear over GR(4) exist if and only if n = (4γ+δ−1)/3 andm = (4γ+2δ−4γ+δ)/6 for some integers γ ≥ 0 and δ > 0. We also prove necessary conditions on (m,n) for 1-perfect codes that are linear over Z4 (we call such codes additive) to exist in D(m,n) graphs; for some of these parameters, we show the existence of codes....
متن کاملOn the number of maximum independent sets in Doob graphs
The Doob graph D(m,n) is a distance-regular graph with the same parameters as the Hamming graph H(2m+n, 4). The maximum independent sets in the Doob graphs are analogs of the distance-2 MDS codes in the Hamming graphs. We prove that the logarithm of the number of the maximum independent sets in D(m,n) grows as 2(1+o(1)). The main tool for the upper estimation is constructing an injective map fr...
متن کاملHyper-self-duality of Hamming and Doob graphs
We show that the Doob and Hamming graphs are hyper-self-dual. We then show that although the Doob graphs are formally dual to certain Hamming graphs, they are not hyper-dual to them. We do so by showing that Bose-Mesner subalgebras and Kronecker products of Bose-Mesner algebras inherit hyper-duality.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1995
ISSN: 0095-8956
DOI: 10.1006/jctb.1995.1046