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On the Computation of the Linear Complexity of a Sequence over GF(q) with Period qnpm

Jianqin Zhou, Jinzhong Li

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Abstract

A fast algorithm is derived for determining the linear complexity and the minimal polynomial of sequences over GF(q) with period qnpm, where p is a prime number, q is a prime number and a primitive root modulo p2. The new algorithm generalizes both the algorithm to compute the linear complexity of sequences over GF(q) with period pm, where p is a prime, q is a prime and a primitive root modulo p2, and the algorithm to compute the linear complexity of sequences over GF(2) with period 2npm, where p is a prime, and 2 is a primitive root modulo p2.

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What this paper is about

A fast algorithm is derived for determining the linear complexity and the minimal polynomial of sequences over GF(q) with period qnpm, where p is a prime number, q is a prime number and a primitive root modulo p2. The new algorithm generalizes both the algorithm to compute the linear complexity of sequences over GF(q) with period pm, where p is a prime, q is a prime and a primitive root modulo p2, and the algorithm to compute the linear complexity of sequences over GF(2) with period 2npm, where p is a prime, and 2 is a primitive root modulo p2.

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Available abstract

A fast algorithm is derived for determining the linear complexity and the minimal polynomial of sequences over GF(q) with period qnpm, where p is a prime number, q is a prime number and a primitive root modulo p2. The new algorithm generalizes both the algorithm to compute the linear complexity of sequences over GF(q) with period pm, where p is a prime, q is a prime and a primitive root modulo p2, and the algorithm to compute the linear complexity of sequences over GF(2) with period 2npm, where p is a prime, and 2 is a primitive root modulo p2.

Key concepts: Modulo, Prime (order theory), Primitive root modulo n, Combinatorics, Sequence (biology), Discrete mathematics, Algorithm, Mathematics

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