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A new family of AMDS symbol-pair constacyclic codes of length $$textbf{4p}$$ and symbol-pair distance $$textbf{9}$$
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2025-02-27 DOI: 10.1007/s10623-025-01600-4
Hai Q. Dinh, Hieu V. Ha, Bac T. Nguyen, Thieu N. Vo
{"title":"A new family of AMDS symbol-pair constacyclic codes of length $$textbf{4p}$$ and symbol-pair distance $$textbf{9}$$","authors":"Hai Q. Dinh, Hieu V. Ha, Bac T. Nguyen, Thieu N. Vo","doi":"10.1007/s10623-025-01600-4","DOIUrl":"https://doi.org/10.1007/s10623-025-01600-4","url":null,"abstract":"<p>Let <i>p</i> be any prime number such that <span>(pequiv 1 pmod 4)</span>, and let <span>({mathbb {F}}_p)</span> be the finite field of <i>p</i> elements. In this paper, we first construct a new AMDS symbol-pair cyclic code of length 4<i>p</i> and of symbol-pair distance 9 by examining its generator polynomial. We then use the generator polynomial to obtain a family of <span>((p-1)/2)</span> AMDS symbol-pair constacyclic codes of the same length and of the same symbol-pair distance.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"51 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143506852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Introducing locality in some generalized AG codes
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2025-02-24 DOI: 10.1007/s10623-025-01597-w
Bastien Pacifico
{"title":"Introducing locality in some generalized AG codes","authors":"Bastien Pacifico","doi":"10.1007/s10623-025-01597-w","DOIUrl":"https://doi.org/10.1007/s10623-025-01597-w","url":null,"abstract":"<p>In 1999, Xing, Niederreiter and Lam introduced a generalization of AG codes (GAG codes) using the evaluation at non-rational places of a function field. In this paper, we show that one can obtain a locality parameter <i>r</i> in such codes by using only non-rational places of degree at most <i>r</i>. This is, up to the author’s knowledge, a new way to construct locally recoverable codes (LRCs). We give an example of such a code reaching the Singleton-like bound for LRCs, and show the parameters obtained for some longer codes over <span>(mathbb F_3)</span>. We then investigate similarities with some concatenated codes. Contrary to previous methods, our construction allows one to obtain directly codes whose dimension is not a multiple of the locality. Finally, we give an asymptotic study using the Garcia–Stichtenoth tower of function fields, for both our construction with GAG codes and a construction of concatenated codes. We give explicit infinite families of LRCs with locality 2 over any finite field of cardinality greater than 3 following our approach with GAG codes.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"24 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143485891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounds and constructions of optimal symbol-pair codes with constant pair-weight
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2025-02-22 DOI: 10.1007/s10623-025-01598-9
Mengzhen Zhao, Yanxun Chang
{"title":"Bounds and constructions of optimal symbol-pair codes with constant pair-weight","authors":"Mengzhen Zhao, Yanxun Chang","doi":"10.1007/s10623-025-01598-9","DOIUrl":"https://doi.org/10.1007/s10623-025-01598-9","url":null,"abstract":"<p>Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against pair errors in symbol-pair read channels. This special channel structure is motivated by the limitations of the reading process in high density data storage systems, where it is no longer possible to read individual symbols. In this work, we study bounds and constructions of codes in symbol-pair metric. By using some combinatorial structures, we give constructions of optimal <i>q</i>-ary symbol-pair codes with constant pair-weight <span>(w_p)</span> and pair-distance <span>(2w_p-1)</span> for some length <i>n</i>, and some optimal <i>q</i>-ary codes with pair-weight <span>(w_p=3,4)</span> for all pair-distance between 3 and <span>(2w_p-1)</span>.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"28 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143470740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal two-dimensional multilength optical orthogonal codes via compatible mixed difference packing set systems
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2025-02-18 DOI: 10.1007/s10623-025-01587-y
Hengming Zhao, Rongcun Qin, Minquan Cheng, Dianhua Wu
{"title":"Optimal two-dimensional multilength optical orthogonal codes via compatible mixed difference packing set systems","authors":"Hengming Zhao, Rongcun Qin, Minquan Cheng, Dianhua Wu","doi":"10.1007/s10623-025-01587-y","DOIUrl":"https://doi.org/10.1007/s10623-025-01587-y","url":null,"abstract":"<p>Two-dimensional multilength optical orthogonal codes (2D MLOOCs) were proposed as a means of simultaneously reducing the chip rate and accommodating multimedia services with multiple bit rates and quality of service (QoS) requirements in OCDMA networks. This paper considers two-dimensional multilength optical orthogonal codes with inter-cross-correlation of <span>(lambda =2)</span>. New upper bounds on the size of 2D MLOOCs are presented under certain constraints. In order to construct optimal 2D MLOOCs, a compatible mixed difference packing (CMDP) set system is introduced. By using both direct constructions and recursive constructions, several series of 2D MLOOCs are obtained which are optimal with respect to the new upper bounds.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"24 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143435691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note on the Walsh spectrum of the Flystel
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2025-02-15 DOI: 10.1007/s10623-025-01589-w
Matthias Johann Steiner
{"title":"A note on the Walsh spectrum of the Flystel","authors":"Matthias Johann Steiner","doi":"10.1007/s10623-025-01589-w","DOIUrl":"https://doi.org/10.1007/s10623-025-01589-w","url":null,"abstract":"<p><span>Anemoi</span> is a family of compression and hash functions over finite fields <span>(mathbb {F}_q)</span> for efficient Zero-Knowledge applications. Its round function is based on a novel permutation <span>(mathcal {H}: mathbb {F}_q^2 rightarrow mathbb {F}_q^2)</span>, called the open <span>Flystel</span>, which is parametrized by a permutation <span>(E: mathbb {F}_q rightarrow mathbb {F}_q)</span> and two functions <span>(Q_gamma , Q_delta : mathbb {F}_q rightarrow mathbb {F}_q)</span>. Over a prime field <span>(mathbb {F}_p)</span> with <i>E</i> a power permutation and <span>(Q_gamma )</span>, <span>(Q_delta )</span> quadratic functions with identical leading coefficient, the <span>Anemoi</span> designers conjectured for the absolute value of the Walsh transform that <span>(max _{textbf{a} in mathbb {F}_p^2, textbf{b} in mathbb {F}_p^2 {setminus } { textbf{0} }} left| mathcal {W}_mathcal {H} (psi , textbf{a}, textbf{b}) right| le p cdot log left( p right) )</span>. By exploiting that the open <span>Flystel</span> is CCZ-equivalent to the closed <span>Flystel</span>, we prove in this note that <span>(max _{textbf{a} in mathbb {F}_p^2, textbf{b} in mathbb {F}_p^2 {setminus } { textbf{0} }} left| mathcal {W}_mathcal {H} (psi , textbf{a}, textbf{b}) right| le (d - 1) cdot p)</span>, where <span>(d = deg left( E right) )</span>.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"13 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143418515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A generalized construction of variable-length non-overlapping codes
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2025-02-15 DOI: 10.1007/s10623-025-01585-0
Chunyan Qin, Gaojun Luo
{"title":"A generalized construction of variable-length non-overlapping codes","authors":"Chunyan Qin, Gaojun Luo","doi":"10.1007/s10623-025-01585-0","DOIUrl":"https://doi.org/10.1007/s10623-025-01585-0","url":null,"abstract":"<p>Non-overlapping codes over a given alphabet are defined as a set of words satisfying the property that no prefix of any length of any word is a suffix of any word in the set, including itself. When the word lengths are variable, it is additionally required that no word is contained as a subword within any other word. In this paper, we present a new construction of variable-length non-overlapping codes that generalizes the construction by Bilotta. Subsequently, we derive the generating function and an enumerative formula for our constructed code, and establish upper bound on their cardinalities. A comparison with the bound provided by Bilotta shows that the newly constructed code offers improved performance in the code size.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"53 4 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143418516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strongly regular graphs decomposable into a divisible design graph and a Delsarte clique
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2025-02-14 DOI: 10.1007/s10623-024-01563-y
Alexander L. Gavrilyuk, Vladislav V. Kabanov
{"title":"Strongly regular graphs decomposable into a divisible design graph and a Delsarte clique","authors":"Alexander L. Gavrilyuk, Vladislav V. Kabanov","doi":"10.1007/s10623-024-01563-y","DOIUrl":"https://doi.org/10.1007/s10623-024-01563-y","url":null,"abstract":"<p>In a previous paper, the authors determined the parameters of all strongly regular graphs that can be decomposed into a divisible design graph and a Hoffman coclique. As a counterpart of this result, in the present paper we determine the parameters of all strongly regular graphs that can be decomposed into a divisible design graph and a Delsarte clique. In particular, an infinite family of strongly regular graphs with the required decomposition and a new infinite family of divisible design graphs are found.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"20 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143417489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Constructions of complete permutations in multiplication
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2025-02-14 DOI: 10.1007/s10623-025-01593-0
Kangquan Li
{"title":"Constructions of complete permutations in multiplication","authors":"Kangquan Li","doi":"10.1007/s10623-025-01593-0","DOIUrl":"https://doi.org/10.1007/s10623-025-01593-0","url":null,"abstract":"<p>Complete permutations in addition over finite fields have attracted many scholars’ attention due to their wide applications in combinatorics, cryptography, sequences, and so on. In 2020, Tu et al. introduced the concept of the complete permutation in the sense of multiplication (CPM for short). In this paper, we further study the constructions and applications of CPMs. We mainly construct many classes of CPMs through three different approaches, i.e., index, self-inverse binomial, which is a new concept proposed in this paper, and linearized polynomial. Particularly, we provide a modular algorithm to produce all CPMs with a given index and determine all CPMs with index 3. Many infinite classes of complete self-inverse binomials are proposed, which explain most of the experimental results about complete self-inverse binomials over <span>({mathbb {F}}_{2^n})</span> with <span>(nle 10)</span>. Six classes of linearized CPMs are given by using standard arguments from fast symbolic computations and a general method is proposed by the AGW criterion. Finally, two applications of CPMs in cryptography are discussed.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"11 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143417488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Probabilistic results on the 2-adic complexity
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2025-02-14 DOI: 10.1007/s10623-025-01592-1
Zhixiong Chen, Arne Winterhof
{"title":"Probabilistic results on the 2-adic complexity","authors":"Zhixiong Chen, Arne Winterhof","doi":"10.1007/s10623-025-01592-1","DOIUrl":"https://doi.org/10.1007/s10623-025-01592-1","url":null,"abstract":"<p>This work is devoted to solving some closely related open problems on the average and asymptotic behavior of the 2-adic complexity of binary sequences. First, for fixed <i>N</i>, we prove that the expected value <span>(E^{text {2-adic}}_N)</span> of the 2-adic complexity over all binary sequences of length <i>N</i> is close to <span>(frac{N}{2})</span> and the deviation from <span>(frac{N}{2})</span> is at most of order of magnitude <span>(log (N))</span>. More precisely, we show that </p><span>$$begin{aligned} frac{N}{2}-1 le E^{text {2-adic}}_N= frac{N}{2}+O(log (N)). end{aligned}$$</span><p>We also prove bounds on the expected value of the <i>N</i>th rational complexity. Our second contribution is to prove for a random binary sequence <span>(mathcal {S})</span> that the <i>N</i>th 2-adic complexity satisfies with probability 1 </p><span>$$begin{aligned} lambda _{mathcal {S}}(N)=frac{N}{2}+O(log (N)) , hbox { for all} N. end{aligned}$$</span>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"80 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143417491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Secret and shared keys recovery on hamming quasi-cyclic with SASCA
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2025-02-12 DOI: 10.1007/s10623-025-01575-2
Chloé Baïsse, Antoine Moran, Guillaume Goy, Julien Maillard, Nicolas Aragon, Philippe Gaborit, Maxime Lecomte, Antoine Loiseau
{"title":"Secret and shared keys recovery on hamming quasi-cyclic with SASCA","authors":"Chloé Baïsse, Antoine Moran, Guillaume Goy, Julien Maillard, Nicolas Aragon, Philippe Gaborit, Maxime Lecomte, Antoine Loiseau","doi":"10.1007/s10623-025-01575-2","DOIUrl":"https://doi.org/10.1007/s10623-025-01575-2","url":null,"abstract":"<p>Soft Analytical Side Channel Attacks (SASCA) are a powerful family of Side Channel Attacks (SCA) that allows the recovery of secret values with only a small number of traces. Their effectiveness lies in the Belief Propagation (BP) algorithm, which enables efficient computation of the marginal distributions of intermediate values. Post-quantum schemes such as Kyber, and more recently, Hamming Quasi-Cyclic (HQC), have been targets of SASCA. Previous SASCA on HQC focused on Reed–Solomon (RS) codes and successfully retrieved the shared key with a high success rate for high noise levels using a single trace. In this work, we present new SASCA on HQC, where both the shared key and the secret key are targeted. Our attacks are realized on simulations. Unlike the previous SASCA, we take a closer look at the Reed–Muller (RM) code. The advantage of this choice is that the RM decoder is applied before the RS decoder, enabling attacks targeting both the secret key and shared key. We build a factor graph of the Fast Hadamard Transform (FHT) function from the HQC reference implementation of April 2023. The information recovered from BP allows us to retrieve the shared key with a single trace. In addition to the previous SASCA targeting HQC, we also manage to recover the secret key with two different chosen ciphertext attacks. One of them requires a single trace and is successful until high noise levels.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"18 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143393286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","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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