Upper Bounds For The Cardinalities Of Two-distance Sets In Euclidean Space Under P-norm

A two-distance set in Ed is a point set X in the d-dimensional Euclideanspace such that the distances between distinct points P and Q in X assume onlytwo different non-zero valuesαorβ. Since 1970s, it has attracted many people'sconcern. Some of them have done a lot of research on this question since it arose.Delsarte, Goethals Seidel and Blokhuis got some results in the method of linearalgebra, these research were all based on the distance that are induced by two-norm. But we all know that the distance induced by two-norm is just a specialcase of the distance induced by p-norm. In this passage, I did some research onthe case that is based on p-norm in the linear algebra method. As the result of theresearch, I found a few of upper bounds of the two-distance set in Euclidean spaceand gave the proof of related conclusion.