Special Distribution of the Shortest Linear Recurring Sequences in Z /(p) Field
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In this paper, the distribution of the shortest linear recurring sequences in Z /(p) is studied. It is found that the shortest linear recurrent length is always equal to n / 2 when n is even and is always equal to n / 2+1 when n is odd for any sequence whose length is n. In other words, the shortest linear recurring length is always equal to the half of the length of the given sequence. The probability of finding the distribution of the shortest linear recurring length of two sequences in Z / (p) field is also given.
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