| Summary: | 碩士 === 淡江大學 === 數學學系 === 89 === Given positive intergers r, s, u, and v, an (r,s;u,v) Perfect map (PM) is defined to be a periodic r by s binary array in which every u by v binary array appears exactly once as a periodic
A de Bruijn sequence for v (in 0’s and 1’s) is a sequence of 2^(v) bits having the property that if s is a bit string of length v, for some m, s = a_(m)a_(m+1)…a_(m+v-1) , and we define for i = 0,…,2^(v).
If s is a c-ary cycle of period n, then we say that s is a v-window sequence if no c-ary v-tuple occurs in two distinct positions within a period of s. A c-ary de Bruijn sequence of span v is a v-window sequence of period equal to c^(v). That is, every possible c-ary v-tuple occurs precisely once in a period c^(v) of the de Bruijn sequence , it is denoted by (c^(v),c,v) de Bruijn sequence. A (2^(v),2,v) de Bruijn sequence can be viewed as a (2^(v),1;v,1) PM or (1,2^(v);1,v)PM.
In this thesis , we construct a (4^(v),4,v) de Bruijn sequence B by using a (2^(v),2,v) de Bruijn sequence A , for v≧1.
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