New Family Of Binary Sequences Research Articles

Linear Complexity of New Binary Sequence Derived From Polynomial Quotients Modulo p in General Case and Their Generalizations

Pseudorandom sequences with large linear complexity have been widely applied in electronic countermeasures, mobile communication and cryptography. Linear complexity is considered as a primary security criterion to measure the unpredictability of pseudorandom sequences. This paper presents the linear complexity and minimal polynomial of a new family of binary sequences derived from polynomial quotients modulo an odd prime <i>p</i> in general case. Results indicate that the sequences have high linear complexity, which means they can resist the linear attack against pseudo-noise or stream ciphers. Moreover, we generalize the result to the polynomial quotients modulo a power of <i>p</i> in general case. Finally, we design a Gpqs stream cipher generator based on the generalized binary pseudorandom sequences.

On the linear complexity of new generalized cyclotomic binary sequences of period p n q m

Sequences with high linear complexity are of importance in different applications. These sequences can be derived from generalized cyclotomic classes. In this paper, we construct new families of binary sequences of period p n q m using new generalized cyclotomic classes, as well as study the linear complexity of these sequences. We obtain the estimate of the linear complexity of new sequences and show that they have high linear complexity for m + n > 2.

Another New Family of Binary Sequences with Six or eight-valued Correlations

In this correspondence, for a positive even integer n, a new family of binary sequences with 2n + 1 sequences of length 2n — 1 taking six and eight valued correlations is presented. This family can be considered as a new class of Gold-like sequences.

Families of p-ary sequences with low correlation and large linear complexity

This paper generalizes a method of generating shift sequences in the interleaved construction proposed by Gong. With the new shift sequences, some new families of p-ary sequences with desired properties can be obtained. A lower bound on the number of new families of binary sequences is also established.

A Class of Large Family of Binary Sequences with Low Correlation and Large Linear Span

In this paper, a new family of binary sequences of period is proposed, where and . The presented family takes 7-valued correlation values , , , , , and . For and , it is proved that the proposed sequence family has linear spans , where l = 2, 3, 4, 5, 6, 7, and the distribution of linear span of sequences in is determined.

5-값 상호상관관계를 갖는 새로운 비선형 이진수열군의 설계와 선형스팬 분석

The design of PN(Pseudo Noise) sequences with good cross-correlation properties is important for many research areas in communication systems. In this paper we propose new family of binary sequences $S^r

A Family of Binary Sequences with 4-Valued Low Correlation and Large Linear Span

For n≡0mod 4,based on d-form function,a new family of binary sequences with period 2n-1 and four-valued low correlation is proposed.The correlation distribution of the proposed family is completely determined.The linear spans of the new sequences are proved to be large and their exact values are also obtained.Compared with the known sequence families,the new family has not only low correlation,but also much larger linear spans.This family of sequences is suitable for cryptography and CDMA systems.

New Families of Binary Sequences with Low Correlation and Large Size

In this paper, for odd n and any k with gcd(n, k) = 1, new binary sequence families Sk of period 2n-1 are constructed. These families have maximum correlation $1+2^{n+3\\over 2}$, family size 22n+2n+1 and maximum linear span $n(n+1)\\over 2$. The correlation distribution of Sk is completely determined as well. Compared with the modified Gold codes with the same family size, the proposed families have the same period and correlation properties, but larger linear span. As good candidates with low correlation and large family size, the new families contain the Gold sequences and the Gold-like sequences. Furthermore, Sk includes a subfamily $\\mathcal{S}^k_1$ which has the same period, correlation distribution, family size and linear span as the family So(2) recently constructed by Yu and Gong. In particular, when k=1, $\\mathcal{S}^k_1$ is exactly So(2).

New family of binary sequences of period 4(2 n − 1) with low correlation

A new family of binary sequences of period 4(2 n −1) with low correlation is constructed for integer n = em. Especially, we obtain a new family with family size 2 n and maximum nontrivial correlation magnitude $${2^{n+3\over 2}+4}$$for odd m and e = 1. Each sequence in the family is constructed by the interleaving of four GKW-like sequences and a perfect sequence. The correlation distribution and linear spans of the sequences are also determined for odd m.

Construction of Even Length Binary Sequences With Asymptotic Merit Factor $6$

Starting with the family of Legendre sequences of length p, Parker constructed a new family of binary sequences of length 2p with good negacyclic correlation properties. Computer calculations indicated that the asymptotic merit factor of his family is 6. In this correspondence a simple version of Parker's construction is given and further applied to Jacobi and modified Jacobi sequences. It is then proven that each of the families constructed, including Parker's, has asymptotic merit factor 6.

New Family of Binary Sequences with Low Correlation

In this paper, a new family of binary sequences of period 2n-1 with low correlation is proposed for integer n = em and even m. The new family has family size 2n + 1 and maximum nontrivial correlation 2n+e/2 + 1 and 2n+e-1/2 + 1 for even and odd e respectively. Especially, for n = 2m and 3m, we obtain a new family of binary sequences with maximum nontrivial correlation 2n/2 + 1 + 1, and the obtained family is one of the binary families with best correlation among the known families with family size no less than their period 2n-1 for even n. Moreover, the correlation distribution of the new family is also determined.

New families of binary sequences with low correlation

For a positive integer, n, new families, S and U, of binary sequences of period 2/sup n/-1 with low correlations are proposed, where for some positive integer, e, S is defined for odd n/e and U for even n/e. The family S has four-valued correlations and is a generalization of the family of Gold-like sequences introduced by S. Boztas and P.V. Kumar (see ibid., vol.40, p.532-7, 1994). The family U, which is also a generalization of the sequence family defined by P. Udaya (Polyphase and frequency hopping sequences obtained from finite rings, Ph.D. dissertation, Dept. Elec. Eng., Indian Inst. Technol., Kanpur, 1992), has six-valued correlations. The relationship between Gold-like sequences and Gold sequences is the same as the relationship between the family S and the family constructed from the binary sequences partially contributed by R. Gold (see ibid., vol.IT-14, p.154-6, 1968), T. Kasami (see Coordinated Sci. Lab., Univ. of Illinois,Urbana-Champaign, Tech. Rep. R-285, AD 632574, 1966), and Welch. Using a lifting idea (No, J.-S. and Kumar, P.V., ibid., vol.35, p.371-9, 1989) for the families S and U, families of binary sequences with the same correlation distributions and large linear span are also constructed.

Generalized construction of binary bent sequences with optimal correlation property

We generalize the construction method of the family of binary bent sequences introduced by Olsen, Scholtz, and Welch (1982) to obtain a family of generalized binary bent sequences with optimal correlation and balance property by using the modified trace transform. Then, the conventional binary bent sequence becomes a special case of our construction method. Several families of the generalized binary bent sequences are constructed by using the bent functions on the intermediate field. Using some of the generalized binary bent sequences, new families of binary sequences with optimal correlation and balance property can be constructed by the lifting idea similar to No (1988) sequences, which are referred to as binary bent-lifted sequences.

Pseudonoise codes constructed by Legendre sequence

A new family of binary sequences is constructed by Legendre sequence with period P, P=3 (mod 4). The new signal set includes two subsets consisting of (P−1)/2 and (P+1)/2 codes with good balance property. A conjecture about the maximum over all (non–trivial) autocorrelation and crosscorrelation values of sequence contained within the two subsets is proposed.

New families of binary sequences with optimal three-level autocorrelation

In this correspondence we give several new families of binary sequences of period N with optimal three-level autocorrelation, where N/spl equiv/2 (mod 4). These sequences are either balanced or almost balanced. Our construction is based on cyclotomy.