Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A Euclidean code is a finite set of points in n-dimensional Euclidean space /spl Rscr//sup n/. The total number of nearest neighbors of a given codepoint in the code is called its touching number.  show that the maximum number of codepoints F/sub n/ that can share the same nearest-neighbor codepoint is equal to the maximum kissing number /spl tau//sub n/ in n dimensions, that is, the maximum number of unit spheres that can touch a given unit sphere without overlapping.  then apply a known upper bound on /spl tau//sub n/ to obtain F/sub n//spl les/2/sup n(0.401+o(1))/, which improves upon the best known upper known upper bound of F/sub n//spl les/2/sup n(1+o(1))/.  also show that the average touching number T of all the points in a Euclidean code is upper bounded /spl tau//sub n/. >
['Kenneth Zeger', 'Allen Gersho']
I am writing a research paper on a idea Number of nearest neighbors in a Euclidean code
[{"from": "human", "value": "I am writing a research paper on a idea Number of nearest neighbors in a Euclidean code"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A Euclidean code is a finite set of points in n-dimensional Euclidean space /spl Rscr//sup n/. The total number of nearest neighbors of a given codepoint in the code is called its touching number.  show that the maximum number of codepoints F/sub n/ that can share the same nearest-neighbor codepoint is equal to the maximum kissing number /spl tau//sub n/ in n dimensions, that is, the maximum number of unit spheres that can touch a given unit sphere without overlapping.  then apply a known upper bound on /spl tau//sub n/ to obtain F/sub n//spl les/2/sup n(0.401+o(1))/, which improves upon the best known upper known upper bound of F/sub n//spl les/2/sup n(1+o(1))/.  also show that the average touching number T of all the points in a Euclidean code is upper bounded /spl tau//sub n/. >"}]