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Geometric progressions in vector sumsets over finite fields
Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2020-09-14 , DOI: 10.1016/j.ffa.2020.101747 Igor E. Shparlinski
中文翻译:
向量求和集在有限域上的几何级数
更新日期:2020-09-14
Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2020-09-14 , DOI: 10.1016/j.ffa.2020.101747 Igor E. Shparlinski
Given two subsets of the d dimensional vector space over the finite field of q elements, we show that the sumset contains k distinct vectors of the form , where , with nonzero vectors , whenever for some constant which depends only on k. This improves the previous result of O. Ahamadi and I.E. Shparlinski (2007), which has the exponent .
中文翻译:
向量求和集在有限域上的几何级数
给定两个子集 所述的d有限域维向量空间的q个元素,我们表明包含以下形式的k个不同向量,在哪里 ,具有非零向量 无论何时 对于一些常数 仅取决于k。这改善了O. Ahamadi和IE Shparlinski(2007)的先前结果,该结果具有指数。