행의 무게가 일정한 이진 (w,r)-중첩 부호 연구

Abstract

Let X be a finite set with T elements and F be a family of subsets of X such that no intersection of w members of the family is covered by a union of r others, where lFI=N. The incidence matrix C of the family F is called a (binary) (w,r)-superimposed code of size N×T. For a given N×T (w,r)-superimposed code, resulting code obtained from the given (w,r)-superimposed code by inserting a new row or deleting any column is also a (w,r)-superimposed code. For a given T, w and r, we denote N(T:w,r) by the minimal number of rows of (w,r)-superimposed code with T columns. An N(T:w,r)×T (w,r)-superimposed code is called an optimal code. For a (w,r)-superimposed code C, C is called a (w,r)-superimposed code with constant weight k if the weight of rows of C is constant k. For a given T, w, r and k, we denote N(T:w,r,k) by the minimal number of rows of (w,r)-superimposed code with T columns and constant weight k. In this thesis, we find the lower bound of N(T:w,r,k) and study when the equality holds.