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Hai Q. Dinh Xiaoqiang Wang Hongwei Liu Songsak Sriboonchitta 《Discrete Mathematics》2019,342(11):3062-3078
Let be an odd prime, and be a nonzero element of the finite field . The -constacyclic codes of length over are classified as the ideals of quotient ring in terms of their generator polynomials. Based on these generator polynomials, the symbol-pair distances of all such -constacyclic codes of length are obtained in this paper. As an application, all MDS symbol-pair constacyclic codes of length over are established, which produce many new MDS symbol-pair codes with good parameters. 相似文献
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The -additive codes are subgroups of , and can be seen as linear codes over when , -additive codes when , or -additive codes when . A -linear generalized Hadamard (GH) code is a GH code over which is the Gray map image of a -additive code. Recursive constructions of -additive GH codes of type with are known. In this paper, we generalize some known results for -linear GH codes with to any prime when , and then we compare them with the ones obtained when . First, we show for which types the corresponding -linear GH codes are nonlinear over . Then, for these codes, we compute the kernel and its dimension, which allow us to classify them completely. Moreover, by computing the rank of some of these codes, we show that, unlike -linear Hadamard codes, the -linear GH codes are not included in the family of -linear GH codes with when prime. Indeed, there are some families with infinite nonlinear -linear GH codes, where the codes are not equivalent to any -linear GH code with . 相似文献
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In this article, we study the structure of finitely ramified mixed characteristic valued fields. For any two complete discrete valued fields and of mixed characteristic with perfect residue fields, we show that if the n-th residue rings are isomorphic for each , then and are isometric and isomorphic. More generally, for , there is depending only on the ramification indices of and such that any homomorphism from the -th residue ring of to the -th residue ring of can be lifted to a homomorphism between the valuation rings. Moreover, we get a functor from the category of certain principal Artinian local rings of length n to the category of certain complete discrete valuation rings of mixed characteristic with perfect residue fields, which naturally generalizes the functorial property of unramified complete discrete valuation rings. Our lifting result improves Basarab's relative completeness theorem for finitely ramified henselian valued fields, which solves a question posed by Basarab, in the case of perfect residue fields. 相似文献
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《Discrete Mathematics》2020,343(3):111721
The -additive codes are subgroups of , and can be seen as a generalization of linear codes over and . A -linear Hadamard code is a binary Hadamard code which is the Gray map image of a -additive code. A partial classification of these codes by using the dimension of the kernel is known. In this paper, we establish that some -linear Hadamard codes of length are equivalent, once is fixed. This allows us to improve the known upper bounds for the number of such nonequivalent codes. Moreover, up to , this new upper bound coincides with a known lower bound (based on the rank and dimension of the kernel). Finally, when we focus on , the full classification of the -linear Hadamard codes of length is established by giving the exact number of such codes. 相似文献
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Given a simple graph with vertex set and edge set , the mixed graph is obtained from by orienting some of its edges. Let denote the Hermitian adjacency matrix of and be the adjacency matrix of . The -rank (resp. rank) of (resp. ), written as (resp. ), is the rank of (resp. ). Denote by the dimension of cycle space of , that is , where denotes the number of connected components of . In this paper, we concentrate on the relation between the -rank of and the rank of . We first show that for every mixed graph . Then we characterize all the mixed graphs that attain the above lower (resp. upper) bound. By these obtained results in the current paper, all the main results obtained in Luo et al. (2018); Wong et al. (2016) may be deduced consequently. 相似文献
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《Discrete Mathematics》2020,343(4):111696
For a set the -neighbourhood of is , where denotes the usual graph distance on . Harper’s vertex-isoperimetric theorem states that among the subsets of given size, the size of the -neighbourhood is minimised when is taken to be an initial segment of the simplicial order. Aubrun and Szarek asked the following question: if is a subset of given size for which the sizes of both and are minimal for all , does it follow that is isomorphic to an initial segment of the simplicial order?Our aim is to give a counterexample. Surprisingly it turns out that there is no counterexample that is a Hamming ball, meaning a set that lies between two consecutive exact Hamming balls, i.e. a set with for some . We go further to classify all the sets for which the sizes of both and are minimal for all among the subsets of of given size. We also prove that, perhaps surprisingly, if for which the sizes of and are minimal among the subsets of of given size, then the sizes of both and are also minimal for all among the subsets of of given size. Hence the same classification also holds when we only require and to have minimal size among the subsets of given size. 相似文献
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Calvin Deng 《Discrete Mathematics》2019,342(2):540-545
We extend a method of Olsson and Bessenrodt to determine the number of even partitions that are simultaneously -core and -core. When and are distinct primes, this also determines the number of self-associate characters of that are simultaneously defect 0 for and . 相似文献
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For a random walk on we study the asymptotic behaviour of the associated centre of mass process . For lattice distributions we give conditions for a local limit theorem to hold. We prove that if the increments of the walk have zero mean and finite second moment, is recurrent if and transient if . In the transient case we show that has a diffusive rate of escape. These results extend work of Grill, who considered simple symmetric random walk. We also give a class of random walks with symmetric heavy-tailed increments for which is transient in . 相似文献
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《Stochastic Processes and their Applications》2020,130(4):2127-2158
Let be an ergodic diffusion with invariant distribution . Consider the empirical measure where is an Euler scheme with decreasing steps which approximates . Given a test function , we obtain sharp concentration inequalities for which improve the results in Honoré et al. (2019). Our hypotheses on the test function cover many real applications: either is supposed to be a coboundary of the infinitesimal generator of the diffusion, or is supposed to be Lipschitz. 相似文献
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Émeline Schmisser 《Stochastic Processes and their Applications》2019,129(12):5364-5405
In this article, we consider a jump diffusion process , with drift function , diffusion coefficient and jump coefficient . This process is observed at discrete times . The sampling interval tends to 0 and the time interval tends to infinity. We assume that is ergodic, strictly stationary and exponentially -mixing. We use a penalized least-square approach to compute adaptive estimators of the functions and . We provide bounds for the risks of the two estimators. 相似文献