424 research outputs found
Weight distributions of cyclic codes with respect to pairwise coprime order elements
Let be an extension of a finite field with . Let
each be of order in and for .
We define a cyclic code over by
where
and . In this paper,
we present a method to compute the weights of . Further, we determine the weight distributions of the cyclic codes
and .Comment: 18 pages. arXiv admin note: substantial text overlap with
arXiv:1306.527
The Decomposability of Toroidal Graphs without Adjacent Triangles or Short Cycles
A graph G has a (Formula presented.) -decomposition if there is a pair (Formula presented.) such that F is a subgraph of G and D is an acyclic orientation of (Formula presented.), where the maximum degree of F is no more than h and the maximum out-degree of D is no more than d. This paper proves that toroidal graphs having no adjacent triangles are (Formula presented.) -decomposable, and for (Formula presented.), toroidal graphs without i- and j-cycles are (Formula presented.) -decomposable. As consequences of these results, toroidal graphs without adjacent triangles are 1-defective DP-4-colorable, and toroidal graphs without i- and j-cycles are 1-defective DP-3-colorable for (Formula presented.).</p
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