Cryptography and Communications最新文献

The study of aperiodic Hamming correlation (APC) of frequency hopping sequences (FHSs) is a hard problem that has not been paid enough attention in the literature. For low-hit-zone (LHZ) FHSs, the study of APC becomes more difficult. We call them LHZ FHSs under APC (LHZ-APC FHSs). LHZ-APC FHSs are studied for the first time in this paper. First, we establish a bound on the family sizes of LHZ-APC FHS sets. Then we present a method for constructions of LHZ-APC FHS sets based on conventional FHS sets under periodic Hamming correlation (conventional PC FHS sets). By choosing different conventional PC FHS sets, we obtain three classes of LHZ-APC FHS sets whose family sizes are optimal or near optimal according to this new bound. Further, we modify the construction method and get more new LHZ-APC FHS sets with optimal family sizes.

Su, Yang, Zhou, and Tang proposed several new classes of optimal autocorrelation interleaved quaternary sequences with period 2n from the twin-prime sequence pairs or GMW sequence pairs. In this paper, we determine the 4-adic complexity of these quaternary sequences by using the correlation function. Our results show that the 4-adic complexity of these quaternary sequences exceeds (frac{2n-16}{6}), so that they are safe enough to resist the attack of the rational approximation algorithm.

Partial spreads are important in finite geometry and can be used to construct linear codes. From the results in (Des. Codes Cryptogr. 90, 1–15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a partial spread is “big enough”, then the corresponding linear code is minimal. This paper used the sufficient condition in (IEEE Trans. Inf. Theory 44(5), 2010–2017, 1998) to prove the minimality of such linear codes. In the present paper, we use the geometric approach to study the minimality of linear codes constructed from partial spreads in all cases.

We study the Griesmer codes of specific Belov type and construct families of distance-optimal linear codes over ({mathbb {Z}_4}) by using multi-variable functions. We first show that the pre-images of specific Griesmer codes of Belov type under a Gray map (phi ) from ({mathbb {Z}_4}) to (mathbb {Z}_2^2) are non-linear except one case. Therefore, we are interested in finding subcodes of Griesmer codes of specific Belov type with maximum possible dimension whose pre-images under (phi ) are still linear over ({mathbb {Z}_4}) such that they also have good properties such as optimality and two-weight. To this end, we introduce a new approach for constructing linear codes over ({mathbb {Z}_4}) using multi-variable functions over (mathbb {Z}). This approach has an advantage in explicitly computing the Lee weight enumerator of a linear code over ({mathbb {Z}_4}). Furthermore, we obtain several other families of distance-optimal two-weight linear codes over ({mathbb {Z}_4}) by using a variety of multi-variable functions. We point out that some of our families of distance-optimal codes over ({mathbb {Z}_4}) have linear binary Gray images which are also distance-optimal.

In this paper, we find a necessary and sufficient condition for multi-twisted Reed-Solomon codes to be MDS. In particular, we introduce a new class of MDS double-twisted Reed-Solomon codes (mathcal {C}_{varvec{alpha , t, h, eta }}) with twists (varvec{t} = (1, 2)) and hooks (varvec{h} = (0, 1)) over the finite field (mathbb {F}_q), providing a non-trivial example over (mathbb {F}_{16}) and enumeration over the finite fields of size up to 17. Moreover, we obtain necessary conditions for the existence of multi-twisted Reed-Solomon codes with small dimensional hull. Consequently, we derive conditions for the existence of MDS multi-twisted Reed-Solomon codes with small dimensional hull.

Zero correlation zone (ZCZ) sequence sets play an important role in reducing multi-cell interference in quasi-synchronous code-division multiple access (QS-CDMA) systems. In this paper, we propose two novel classes of ZCZ sequence sets based on orthogonal matrices and uncorrelated ZCZ sequence sets. The subsets of the proposed ZCZ sequence sets are ZCZ sequence sets of their own. Moreover, they display inter-set zero cross-correlation zone (ZCCZ) among two different subsets. The proposed ZCZ sequence sets are optimal with respect to the Tang-Fan-Matsufuji bound.

In this paper, for the first time, we present a direct construction of multiple zero-correlation zone (ZCZ) sequence sets with inter-set zero-cross correlation zone (ZCCZ) from a generalised Boolean function. Tang et al., in their 2010 paper, proposed an open problem to construct N binary ZCZ sequence sets such that each of these ZCZ sequence sets is optimal and the union of these N sets is again an optimal ZCZ sequence set. The proposed construction partially settles this open problem by presenting a construction of optimal ZCZ sequence sets such that their union is an almost-optimal ZCZ sequence set. The proposed construction is presented by a two-layer graphical representation and compared with the existing state-of-the-art. Moreover, it has been shown that some of the existing constructions are special cases of the proposed construction. Finally, the performance of a novel multi-cell quasi synchronous-code division multiple access (QS-CDMA) system is provided by using the proposed multiple ZCZ sequence sets and it has been compared with a conventional ZCZ-based QS-CDMA system.

Let R be the Galois ring of characteristic 4 and cardinality (4^{m}), where m is a natural number. Let ( mathcal {C} ) be a linear code of length n over R and (Phi ) be the Homogeneous Gray map on (R^n). In this paper, we show that (Phi (mathcal {C})) is linear if and only if for every (varvec{X}, varvec{Y}in mathcal {C} ), (2(varvec{X} odot varvec{Y})in mathcal {C}). Using the generator polynomial of a cyclic code of odd length over R, a necessary and sufficient condition is given which its Gray image is linear.