On the Linear Complexity of Quaternary Cyclotomic Sequences with the Period 2&lt;i&gt;pq&lt;/i&gt;

Chang, Zuling; Li, Dandan

doi:10.1587/transfun.e97.a.679

Cited by 11 publications

(6 citation statements)

References 15 publications

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“…Theorem 9. Let (s u ) u≥0 be the quaternary sequence over Z 4 defined by (1). Then the linear complexity of (s u ) u≥0 satisfies…”

Section: Linear Complexity For the Case P ≡ ±3 (Mod 8)mentioning

confidence: 99%

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Linear complexity and trace representation of quaternary sequences over ℤ 4 $\mathbb {Z}_{4}$ based on generalized cyclotomic classes modulo pq

Chen

2016

Cryptogr. Commun.

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We determine the exact values of the linear complexity of 2pperiodic quaternary sequences over Z 4 (the residue class ring modulo 4) defined from the generalized cyclotomic classes modulo 2p in terms of the theory of of Galois rings of characteristic 4, where p is an odd prime. Compared to the case of quaternary sequences over the finite field of order 4, it is more difficult and complicated to consider the roots of polynomials in Z 4 [X] due to the zero divisors in Z 4 and hence brings some interesting twists. We prove the main results as follows Linear Complexity =

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“…Theorem 9. Let (s u ) u≥0 be the quaternary sequence over Z 4 defined by (1). Then the linear complexity of (s u ) u≥0 satisfies…”

Section: Linear Complexity For the Case P ≡ ±3 (Mod 8)mentioning

confidence: 99%

“…(2) 2 Ke and Zhang extended to define quaternary cyclotomic sequences of length 2p m [13]. Chang and Li defined quaternary cyclotomic sequences of length 2pq [1]. Both are over the finite field F 4 .…”

Section: Introductionmentioning

confidence: 99%

Linear complexity and trace representation of quaternary sequences over ℤ 4 $\mathbb {Z}_{4}$ based on generalized cyclotomic classes modulo pq

Chen

2016

Cryptogr. Commun.

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“…The linear complexity of generalized sequences of period pq and 2pq over the finite field of four elements is presented in Refs. [11,12]. Fan and Ge [13] introduced a generalized cyclotomy of order d over Z p e 1 1 ;p e 2 2 ;:::;p en n , which includes Whiteman's and Ding's generalized cyclotomy as special cases.…”

Section: Introductionmentioning

confidence: 99%

On the linear complexity of new generalized cyclotomic binary sequences of order two and period pqr

Liu¹,

Yang²,

et al. 2016

Tinshhua Sci. Technol.

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Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. Let p, q, and r be distinct odd primes with gcd(p-1, q-1)=gcd(p-1, r -1)=gcd(q-1, r -1)=2. In this paper, a new class of generalized cyclotomic sequence with respect to pqr over GF(2) is constructed by finding a special characteristic set. In addition, we determine its linear complexity using cyclotomic theory. Our results show that these sequences have high linear complexity, which means they can resist linear attacks.

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“…There are plentiful and meaningful conclusions of generalised cyclotomic binary sequences [4][5][6][7][8][9][10][11][12][13][14] and references therein. While there are scattered results of generalised cyclotomic quaternary sequences over F 4 [15][16][17]. Du et al determined the linear complexity of quaternary sequences over F 4 that used generalised cyclotomic classes modulo 2p [15].…”

Section: Introductionmentioning

confidence: 99%

“…The linear complexity of the new class of cyclotomic quaternary sequence over F 4 with period 2p m was studied by Ke [16]. Chang and Li gave the linear complexity of cyclotomic quaternary sequence over F 4 with period 2pq [17]. The constructed sequences over F 4 can be divided into two types: a permutation of {0, 1, α,1+α} such as [15] and all permutations of {0, 1, α,1+α} such as [16,17].…”

Section: Introductionmentioning

confidence: 99%

Linear complexity of generalised cyclotomic quaternary sequences of length 2 p ^{m
+1} q ^{n
+1}

Chang

Wen

et al. 2016

IET Information Security

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On the Linear Complexity of Quaternary Cyclotomic Sequences with the Period 2<i>pq</i>

Cited by 11 publications

References 15 publications

Linear complexity and trace representation of quaternary sequences over ℤ 4 $\mathbb {Z}_{4}$ based on generalized cyclotomic classes modulo pq

Linear complexity and trace representation of quaternary sequences over ℤ 4 $\mathbb {Z}_{4}$ based on generalized cyclotomic classes modulo pq

On the linear complexity of new generalized cyclotomic binary sequences of order two and period pqr

Linear complexity of generalised cyclotomic quaternary sequences of length 2 p ^{m
+1} q ^{n
+1}

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On the Linear Complexity of Quaternary Cyclotomic Sequences with the Period 2<i>pq</i>

Cited by 11 publications

References 15 publications

Linear complexity and trace representation of quaternary sequences over ℤ 4 $\mathbb {Z}_{4}$ based on generalized cyclotomic classes modulo pq

Linear complexity and trace representation of quaternary sequences over ℤ 4 $\mathbb {Z}_{4}$ based on generalized cyclotomic classes modulo pq

On the linear complexity of new generalized cyclotomic binary sequences of order two and period pqr

Linear complexity of generalised cyclotomic quaternary sequences of length 2 p m +1 q n +1

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Linear complexity of generalised cyclotomic quaternary sequences of length 2 p ^{m
+1} q ^{n
+1}