Antipodal Gray codes
نویسندگان
چکیده
منابع مشابه
Antipodal Gray codes
An n-bit Gray code is a circular listing of the 2 n-bit strings so that successive strings differ only in one bit position. An n-bit antipodal Gray code has the additional property that the complement of any string appears exactly n steps away in the list. The problem of determining for which values of n antipodal Gray codes can exist was posed by Hunter Snevily, who showed them to be possible ...
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Binary non-antipodal completely regular codes are characterized. Using the result on nonexistence of nontrivial binary perfect codes, it is concluded that there are no unknown nontrivial non-antipodal completely regular binary codes with minimum distance d ≥ 3. The only such codes are halves and punctered halves of known binary perfect codes. Thus, new such codes with covering radiuses ρ = 2, 3...
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A Gray code is a Hamilton path H on the n-cube, Q n. By labeling each edge of Q n with the dimension that changes between its incident vertices, a Gray code can be thought of as a sequence H = t 1 ; t 2 ; : : : ; t N-1 (with N = 2 n and each t i satisfying 1 t i n). The sequence H deenes an (undirected) graph of transitions, G H , whose vertex set is f1; 2; : : : ; ng and whose edge set E(G H) ...
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We show three main results concerning Hamiltonicity of graphs derived from antimatroids. These results provide Gray codes for the feasible sets and basic words of antimatroids. For antimatroid (E; F), let J (F) denote the graph whose vertices are the sets of F, where two vertices are adjacent if the corresponding sets diier by one element. Deene J (F; k) to be the subgraph of J (F) 2 induced by...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/j.disc.2003.07.012