1. Studies on the distribution of the shortest linear recurring sequences
- Author
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Yin, Qian, Yuan, Zhi-Yong, and Guo, Ping
- Subjects
- *
RECURSIVE sequences (Mathematics) , *DISTRIBUTION (Probability theory) , *NUMERICAL calculations , *ALGORITHMS , *MATHEMATICAL analysis , *INFORMATION theory , *PROBLEM solving - Abstract
Abstract: The distribution of the shortest linear recurrence (SLR) sequences in the Z/(p) field and over the Z/(p e ) ring is studied. It is found that the length of the shortest linear recurrent (SLRL) is always equal to n/2, if n is even and n/2+1 if n is odd in the Z/(p) field, respectively. On the other hand, over the Z/(p e ) ring, the number of sequences with length n can also be calculated. The recurring distribution regulation of the shortest linear recurring sequences is also found. To solve the problem of calculating the SLRL, a new simple representation of the Berlekamp–Massey algorithm is developed as well. [Copyright &y& Elsevier]
- Published
- 2009
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