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Low-hit-zone frequency hopping sequence sets under aperiodic Hamming correlation 非周期性汉明相关性下的低命中区跳频序列集
Cryptography and Communications Pub Date : 2024-01-03 DOI: 10.1007/s12095-023-00691-x
Xing Liu
{"title":"Low-hit-zone frequency hopping sequence sets under aperiodic Hamming correlation","authors":"Xing Liu","doi":"10.1007/s12095-023-00691-x","DOIUrl":"https://doi.org/10.1007/s12095-023-00691-x","url":null,"abstract":"<p>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.</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139093706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The 4-adic complexity of interleaved quaternary sequences of even period with optimal autocorrelation 具有最佳自相关性的偶数周期交错四元序列的四元复杂性
Cryptography and Communications Pub Date : 2023-12-23 DOI: 10.1007/s12095-023-00690-y
Xiaoyan Jing, Zhefeng Xu
{"title":"The 4-adic complexity of interleaved quaternary sequences of even period with optimal autocorrelation","authors":"Xiaoyan Jing, Zhefeng Xu","doi":"10.1007/s12095-023-00690-y","DOIUrl":"https://doi.org/10.1007/s12095-023-00690-y","url":null,"abstract":"<p>Su, Yang, Zhou, and Tang proposed several new classes of optimal autocorrelation interleaved quaternary sequences with period 2<i>n</i> 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 <span>(frac{2n-16}{6})</span>, so that they are safe enough to resist the attack of the rational approximation algorithm.</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minimal linear codes constructed from partial spreads 由部分传播构建的最小线性编码
Cryptography and Communications Pub Date : 2023-12-13 DOI: 10.1007/s12095-023-00689-5
Xia Wu, Wei Lu, Xiwang Cao, Gaojun Luo
{"title":"Minimal linear codes constructed from partial spreads","authors":"Xia Wu, Wei Lu, Xiwang Cao, Gaojun Luo","doi":"10.1007/s12095-023-00689-5","DOIUrl":"https://doi.org/10.1007/s12095-023-00689-5","url":null,"abstract":"<p>Partial spreads are important in finite geometry and can be used to construct linear codes. From the results in (Des. Codes Cryptogr. <b>90</b>, 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 <b>44</b>(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.</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"98 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138629199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Griesmer codes of Belov type and optimal quaternary codes via multi-variable functions 贝洛夫型格里斯梅尔码和通过多变量函数的最优四元码
Cryptography and Communications Pub Date : 2023-12-07 DOI: 10.1007/s12095-023-00686-8
Jong Yoon Hyun, Nayoung Han, Yoonjin Lee
{"title":"The Griesmer codes of Belov type and optimal quaternary codes via multi-variable functions","authors":"Jong Yoon Hyun, Nayoung Han, Yoonjin Lee","doi":"10.1007/s12095-023-00686-8","DOIUrl":"https://doi.org/10.1007/s12095-023-00686-8","url":null,"abstract":"<p>We study the Griesmer codes of specific Belov type and construct families of distance-optimal linear codes over <span>({mathbb {Z}_4})</span> by using multi-variable functions. We first show that the pre-images of specific Griesmer codes of Belov type under a Gray map <span>(phi )</span> from <span>({mathbb {Z}_4})</span> to <span>(mathbb {Z}_2^2)</span> are <i>non-linear</i> 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 <span>(phi )</span> are still <i>linear</i> over <span>({mathbb {Z}_4})</span> such that they also have good properties such as <i>optimality</i> and <i>two-weight</i>. To this end, we introduce a new approach for constructing linear codes over <span>({mathbb {Z}_4})</span> using multi-variable functions over <span>(mathbb {Z})</span>. This approach has an advantage in explicitly computing the Lee weight enumerator of a linear code over <span>({mathbb {Z}_4})</span>. Furthermore, we obtain several other families of distance-optimal <i>two-weight</i> linear codes over <span>({mathbb {Z}_4})</span> by using a variety of multi-variable functions. We point out that some of our families of distance-optimal codes over <span>({mathbb {Z}_4})</span> have <i>linear</i> binary Gray images which are also distance-optimal.</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138556884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
MDS multi-twisted Reed-Solomon codes with small dimensional hull 具有小尺寸外壳的MDS多扭曲里德-所罗门码
Cryptography and Communications Pub Date : 2023-12-04 DOI: 10.1007/s12095-023-00688-6
Harshdeep Singh, Kapish Chand Meena
{"title":"MDS multi-twisted Reed-Solomon codes with small dimensional hull","authors":"Harshdeep Singh, Kapish Chand Meena","doi":"10.1007/s12095-023-00688-6","DOIUrl":"https://doi.org/10.1007/s12095-023-00688-6","url":null,"abstract":"<p>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 <span>(mathcal {C}_{varvec{alpha , t, h, eta }})</span> with twists <span>(varvec{t} = (1, 2))</span> and hooks <span>(varvec{h} = (0, 1))</span> over the finite field <span>(mathbb {F}_q)</span>, providing a non-trivial example over <span>(mathbb {F}_{16})</span> 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.</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"87 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
New construction of optimal ZCZ sequence sets with inter-set zero cross-correlation zone 具有集间零相互关带的ZCZ序列集的新构造
Cryptography and Communications Pub Date : 2023-11-21 DOI: 10.1007/s12095-023-00685-9
Zheng Wang, Zhifan Ye, Chunming Tang, Yang Yang
{"title":"New construction of optimal ZCZ sequence sets with inter-set zero cross-correlation zone","authors":"Zheng Wang, Zhifan Ye, Chunming Tang, Yang Yang","doi":"10.1007/s12095-023-00685-9","DOIUrl":"https://doi.org/10.1007/s12095-023-00685-9","url":null,"abstract":"<p>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.</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"87 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A new construction of almost-optimal multiple ZCZ sequence sets for multi-cell QS-CDMA system 多小区QS-CDMA系统中几乎最优多个ZCZ序列集的新构造
Cryptography and Communications Pub Date : 2023-11-20 DOI: 10.1007/s12095-023-00684-w
Nishant Kumar, Sudhan Majhi, Sushant K. Jha
{"title":"A new construction of almost-optimal multiple ZCZ sequence sets for multi-cell QS-CDMA system","authors":"Nishant Kumar, Sudhan Majhi, Sushant K. Jha","doi":"10.1007/s12095-023-00684-w","DOIUrl":"https://doi.org/10.1007/s12095-023-00684-w","url":null,"abstract":"<p>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 <i>N</i> binary ZCZ sequence sets such that each of these ZCZ sequence sets is optimal and the union of these <i>N</i> 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.</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Homogeneous Gray image of linear codes over the Galois ring GR(4, m) 伽罗瓦环GR(4,m)上线性码的均匀灰度图像
Cryptography and Communications Pub Date : 2023-11-17 DOI: 10.1007/s12095-023-00683-x
Hamidreza Eyvazi, Karim Samei, Batoul Savari
{"title":"The Homogeneous Gray image of linear codes over the Galois ring GR(4, m)","authors":"Hamidreza Eyvazi, Karim Samei, Batoul Savari","doi":"10.1007/s12095-023-00683-x","DOIUrl":"https://doi.org/10.1007/s12095-023-00683-x","url":null,"abstract":"<p>Let <i>R</i> be the Galois ring of characteristic 4 and cardinality <span>(4^{m})</span>, where <i>m</i> is a natural number. Let <span>( mathcal {C} )</span> be a linear code of length <i>n</i> over <i>R</i> and <span>(Phi )</span> be the Homogeneous Gray map on <span>(R^n)</span>. In this paper, we show that <span>(Phi (mathcal {C}))</span> is linear if and only if for every <span>(varvec{X}, varvec{Y}in mathcal {C} )</span>, <span>(2(varvec{X} odot varvec{Y})in mathcal {C})</span>. Using the generator polynomial of a cyclic code of odd length over <i>R</i>, a necessary and sufficient condition is given which its Gray image is linear.</p>","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the $$sigma $$ duals and $$sigma $$ hulls of linear codes 关于线性码的$$sigma $$对偶和$$sigma $$壳
Cryptography and Communications Pub Date : 2023-11-13 DOI: 10.1007/s12095-023-00679-7
Meng Cao, Jing Yang, Fuchuan Wei
{"title":"On the $$sigma $$ duals and $$sigma $$ hulls of linear codes","authors":"Meng Cao, Jing Yang, Fuchuan Wei","doi":"10.1007/s12095-023-00679-7","DOIUrl":"https://doi.org/10.1007/s12095-023-00679-7","url":null,"abstract":"","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"52 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136346553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Frameproof codes, separable codes and $$B_2$$ codes: Bounds and constructions 防帧代码，可分离代码和$$B_2$$代码:边界和结构
Cryptography and Communications Pub Date : 2023-11-10 DOI: 10.1007/s12095-023-00682-y
Marcel Fernandez, John Livieratos, Sebastià Martín
{"title":"Frameproof codes, separable codes and $$B_2$$ codes: Bounds and constructions","authors":"Marcel Fernandez, John Livieratos, Sebastià Martín","doi":"10.1007/s12095-023-00682-y","DOIUrl":"https://doi.org/10.1007/s12095-023-00682-y","url":null,"abstract":"Abstract In this paper, constructions of frameproof codes, separable codes, and $$B_2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>B</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> codes are obtained. For each family of codes, the Lovász Local Lemmais used to establish lower bounds for the codes. The obtained bounds match all best known bounds in the literature. Our strategy allows us to present constructions of the aforementioned codes, by using the variable framework for the Lovász Local Lemma.","PeriodicalId":10788,"journal":{"name":"Cryptography and Communications","volume":"117 25","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135136576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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