共查询到20条相似文献,搜索用时 531 毫秒
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We use character sums over finite fields to give formulas for the number of solutions of certain diagonal equations of the form We also show that if the value distribution of character sums , , is known, then one can obtain the number of solutions of the system of equations for some particular m. We finally apply our results to induce some facts about Waring's problems and the covering radius of certain cyclic codes. 相似文献
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Let and be a sufficiently large real number. In this paper, we prove that, for almost all , the Diophantine inequality is solvable in primes . Moreover, we also investigate the problem of six primes and prove that the Diophantine inequality is solvable in primes for sufficiently large real number . 相似文献
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Let be a finite field of odd order and , where are positive integers, are distinct odd primes and . In this paper, we study the irreducible factorization of over and all primitive idempotents in the ring .Moreover, we obtain the dimensions and the minimum Hamming distances of all irreducible cyclic codes of length over . 相似文献
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Let e be a positive integer, p be an odd prime, , and be the finite field of q elements. Let . The graph is a bipartite graph with vertex partitions and , and edges defined as follows: a vertex is adjacent to a vertex if and only if and . If and , the graph contains no cycles of length less than eight and is edge-transitive. Motivated by certain questions in extremal graph theory and finite geometry, people search for examples of graphs containing no cycles of length less than eight and not isomorphic to the graph , even without requiring them to be edge-transitive. So far, no such graphs have been found. It was conjectured that if both f and g are monomials, then no such graphs exist. In this paper we prove the conjecture. 相似文献
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