Classification of a class of distance-regular graphs via completely regular codes
نویسندگان
چکیده
منابع مشابه
Classification of a class of distance-regular graphs via completely regular codes
The study of P-polynomial association schemes, or distance-regular graphs, and their possible classification is one of the main topics of algebraic combinatorics. One way to approach the issue is through the parameters Pkij which characterize the scheme. The purpose of this paper is to deal with a concrete case. This case is also important in the study of the links between P-polynomial schemes ...
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In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius ρ equal to 3 or 4, and are 1/2-th parts, for i ∈ {1, . . . , u} of binary (respectively, extended binary) Hamming codes of length n = 2 − 1 (respectively, 2), where m = 2u. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs...
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Infinite families of linear binary nested completely regular codes with covering radius ρ equal to 3 and 4 are constructed. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs of diameter D = 3 or 4 are constructed. In some cases, the constructed codes are also completely transitive codes and the corresponding coset graphs are distance-transitive.
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For each bipartition_of a bipartite distance-regular graph F, there naturally corresponds another distance-regular graph F called a halved graph. It is shown that the existence of a perfect e-code in a halved graph F is equivalent to the existence of a uniformly packed 2e-code in F with certain specific parameters. Using this equivalence, we show the non-existence of perfect codes for two class...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1990
ISSN: 0166-218X
DOI: 10.1016/0166-218x(90)90106-m