Concerning the vector v(m,t) |
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| Institution: | 1. Department of Pharmacy, Pharmaceutical Technology and Parasitology, Faculty of Pharmacy, University of Valencia, Av. Vicent Andrés Estellés s/n, 46100 Burjassot, Valencia, Spain;2. Instituto Interuniversitario de Investigación de Reconocimiento Molecular y Desarrollo Tecnológico (IDM), Universitat Politècnica de València, Universitat de València, Av. Vicent Andrés Estellés s/n, 46100 Burjassot, Valencia, Spain;3. Department of Earth Physics and Thermodynamics, Faculty of Physics, University of Valencia, Av. Vicent Andrés Estellés s/n, 46100 Burjassot, Valencia, Spain;4. Department of Physical Chemistry, Faculty of Pharmacy, University of Valencia, Av. Vicent Andrés Estellés s/n, 46100 Burjassot, Valencia, Spain;5. Department of Pathology, University of Valencia, Av. Blasco Ibañez 17, 46010 Valencia, Spain;1. Center for Advanced Manufacturing & Material Processing, Department of Mechanical Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia;2. Faculty of Mechanical Engineering, Universiti Teknologi Mara, 40450 Shah Alam, Selangor, Malaysia;3. Division of Neurosurgery, Faculty of Medicine, University of Malaya, Kuala Lumpur 50603, Malaysia;4. Centre for Ionics University of Malaya, Department of Physics, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia;5. Ceramics Technology Group, SIRIM Berhad, Shah Alam 40911, Malaysia;1. Mustafa Erdik, Boğaziçi University, İstanbul, Turkey;2. Ülker Consulting Engineering Ltd, İstanbul, Turkey;3. OBS Project Engineering Consulting Ltd., İstanbul, Turkey;4. CT Engineering and Research, İstanbul, Turkey;1. Oklahoma State University, USA;2. California State University, Fullerton, USA |
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| Abstract: | Let q = mt + 1 be a prime power, and let v(m, t) be the (m + 1)-vector (b1, b2, …, bm + 1) of elements of GF(q) such that for each k, 1 ⩽ k ⩽ m + 1, the set {bi−bj:i∈{1,2,…m+1} − {m + 2 − k}, j i + k(mod m + 2) and 1⩽j⩽m+1} forms a system of representatives for the cyclotomic classes of index m in GF(q). In this paper, we investigate the existence of such vectors. An upper bound on t for the existence of a v(m, t) is given for each fixed m unless both m and t are even, in which case there is no such a vector. Some special cases are also considered. |
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