منابع مشابه
Arithmetic completely regular codes
In this paper, we explore completely regular codes in the Hamming graphs and related graphs. Experimental evidence suggests that many completely regular codes have the property that the eigenvalues of the code are in arithmetic progression. In order to better understand these “arithmetic completely regular codes”, we focus on cartesian products of completely regular codes and products of their ...
متن کاملOn non-antipodal binary completely regular codes
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...
متن کاملOn new completely regular q-ary codes
In this paper from q-ary perfect codes new completely regular q-ary codes are constructed. In particular, two new ternary completely regular codes are obtained from ternary Golay [11, 6, 5] code. The first [11, 5, 6] code with covering radius ρ = 4 coincides with the dual Golay code and its intersection array is (22, 20, 18, 2, 1; 1, 2, 9, 20, 22) . The second [10, 5, 5] code, with covering rad...
متن کاملOn nested completely regular codes and distance regular graphs
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.
متن کاملUniqueness of certain completely regular Hadamard codes
We classify binary completely regular codes of length m with minimum distance δ for (m, δ) = (12, 6) and (11, 5). We prove that such codes are unique up to equivalence, and in particular, are equivalent to certain Hadamard codes. We prove that the automorphism groups of these Hadamard codes, modulo the kernel of a particular action, are isomorphic to certain Mathieu groups, from which we prove ...
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ژورنال
عنوان ژورنال: Problems of Information Transmission
سال: 2019
ISSN: 0032-9460,1608-3253
DOI: 10.1134/s0032946019010010