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We explicitly determine generators of cyclic codes over a non-Galois finite chain ring of length , where p is a prime number and k is a positive integer. We completely classify that there are three types of principal ideals of and four types of non-principal ideals of , which are associated with cyclic codes over of length . We then obtain a mass formula for cyclic codes over of length . 相似文献
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Sanming Zhou 《Journal of Pure and Applied Algebra》2019,223(3):931-947
We study two families of cyclotomic graphs and perfect codes in them. They are Cayley graphs on the additive group of , with connection sets and , respectively, where () is an mth primitive root of unity, A a nonzero ideal of , and ? Euler's totient function. We call them the mth cyclotomic graph and the second kind mth cyclotomic graph, and denote them by and , respectively. We give a necessary and sufficient condition for to be a perfect t-code in and a necessary condition for to be such a code in , where is an integer and D an ideal of containing A. In the case when , is known as an Eisenstein–Jacobi and Gaussian networks, respectively, and we obtain necessary conditions for to be a perfect t-code in , where with β dividing α. In the literature such conditions are known to be sufficient when and under an additional condition. We give a classification of all first kind Frobenius circulants of valency 2p and prove that they are all pth cyclotomic graphs, where p is an odd prime. Such graphs belong to a large family of Cayley graphs that are efficient for routing and gossiping. 相似文献
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《Discrete Mathematics》2022,345(11):113058
Given an undirected graph , a conflict-free coloring with respect to open neighborhoods (CFON coloring) is a vertex coloring such that every vertex has a uniquely colored vertex in its open neighborhood. The minimum number of colors required for such a coloring is the CFON chromatic number of G, denoted by .In previous work [WG 2020], we showed the upper bound , where denotes the distance to cluster parameter of G. In this paper, we obtain the improved upper bound of . We also exhibit a family of graphs for which , thereby demonstrating that our upper bound is tight. 相似文献
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The paper investigates longtime dynamics of the Kirchhoff wave equation with strong damping and critical nonlinearities: , with . The well-posedness and the existence of global and exponential attractors are established, and the stability of the attractors on the perturbation parameter ? is proved for the IBVP of the equation provided that both nonlinearities and are of critical growth. 相似文献
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《Discrete Mathematics》2022,345(10):113004
Let G be a graph. We say that G is perfectly divisible if for each induced subgraph H of G, can be partitioned into A and B such that is perfect and . We use and to denote a path and a cycle on t vertices, respectively. For two disjoint graphs and , we use to denote the graph with vertex set and edge set , and use to denote the graph with vertex set and edge set . In this paper, we prove that (i) -free graphs are perfectly divisible, (ii) if G is -free with , (iii) if G is -free, and (iv) if G is -free. 相似文献
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