Fast Algorithms for Determining the Linear Complexity of Period Sequences
نویسندگان
چکیده
We introduce a fast algorithm for determining the linear complexity and the minimal polynomial of a sequence with period p over GF(q) , where p is an odd prime, q is a prime and a primitive root modulo p; and its two generalized algorithms. One is the algorithm for determining the linear complexity and the minimal polynomial of a sequence with period pq over GF(q), the other is the algorithm for determining the k -error linear complexity of a sequence with period p over GF(q), where p is an odd prime, q is a prime and a primitive root modulo p. The algorithm for determining the linear complexity and the minimal polynomial of a sequence with period 2p over GF(q) is also introduced. where p and q are odd prime, and q is a primitive root (mod p). These algorithms uses the fact that in these case the factorization of x − 1 is especially simple for N = p, 2p, pq.
منابع مشابه
Fast Algorithms for Determining the Minimal Polynomials of Sequences with Period kn Over GF(Pm)
A fast algorithm is derived for determining the linear complexity and the minimal polynomials of sequences over GF (p) with period kn, where p is a prime number, gcd(n, p − 1) = 1 and p − 1 = ku, n, k and u are integers. The algorithm presented here covers the algorithm proposed by Chen for determining the minimal polynomials of sequences over GF (p) with period 2n, where p is a prime, gcd(n, p...
متن کاملFast algorithms for determining the linear complexities of sequences over GF (p) with the period 3n
In this paper, for the the primes p such that 3 is a divisor of p − 1, we prove a result which reduces the computation of the linear complexity of a sequence over GF (p)(any positive integer m) with the period 3n (n and p−1 are coprime) to the computation of the linear complexities of three sequences with the period n. Combined with some known algorithms such as generalized Games-Chan algorithm...
متن کاملA Fast Algorithm for Determining the Linear Complexity of Periodic Sequences over GF(3)
Jianqin Zhou (Dept. of Computer Science, Anhui University of Technology, Ma’anshan 243002, P. R. China) (E-mail: [email protected]) Abstract: A fast algorithm is presented for determining the linear complexity and the minimal polynomial of periodic sequences over GF(q) with period q n p m , where p is a prime, q is a prime and a primitive root modulo p. The algorithm presented here generalizes...
متن کاملgpALIGNER: A Fast Algorithm for Global Pairwise Alignment of DNA Sequences
Bioinformatics, through the sequencing of the full genomes for many species, is increasingly relying on efficient global alignment tools exhibiting both high sensitivity and specificity. Many computational algorithms have been applied for solving the sequence alignment problem. Dynamic programming, statistical methods, approximation and heuristic algorithms are the most common methods appli...
متن کاملJu l 2 00 6 Reducing the Computation of Linear Complexities of Periodic Sequences
The linear complexity of a periodic sequence over GF (p) play an important role in cryptography and communication([1]). In this correspondence, we prove a result which reduces the computation of the linear complexity and minimal connection polynomial of an arbitrary period un (where u|p−1, gcd(n, p −1) = 1) sequence over GF (p) to the computation of the linear complexities and minimal connectio...
متن کامل