Open AccessLinear Complexity of d ‐Ary Sequence Derived from Euler Quotients over GF( q )
Author(s) -
Ye Zhifan,
Ke Pinhui,
Chen Zhixiong
Publication year - 2019
Publication title -
chinese journal of electronics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 25
eISSN - 2075-5597
pISSN - 1022-4653
DOI - 10.1049/cje.2019.02.004
Subject(s) - prime (order theory) , sequence (biology) , mathematics , quotient , euler's formula , integer (computer science) , set (abstract data type) , discrete mathematics , prime number , combinatorics , computer science , mathematical analysis , genetics , biology , programming language
For an odd prime p and positive integers r , d such that 0 < d ≤ p r , a generic construction of d ‐ary sequence based on Euler quotients is presented in this paper. Compared with the known construction, in which the support set of the sequence is fixed and d is usually required to be a prime, the support set of the proposed sequence is flexible and d could be any positive integer less then pr in our construction. Furthermore, the linear complexity of the proposed sequence over prime field GF( q ) with the assumption of q p ‐1 ≢ 1 mod p 2 is determined. An algorithm of computing the linear complexity of the sequence is also given. Our results indicate that, with some constrains on the support set, the new sequences possess large linear complexities.