Pub Date : 2023-11-03DOI: 10.1142/s021949882550135x
M. Benelmekki, S. El Baghdadi, S. Najib
{"title":"Factorization in Group Algebras","authors":"M. Benelmekki, S. El Baghdadi, S. Najib","doi":"10.1142/s021949882550135x","DOIUrl":"https://doi.org/10.1142/s021949882550135x","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135868022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1142/s0219498825501348
Septimiu Crivei, Robert Pop
{"title":"Projectivity and Subprojectivity Domains in Exact Categories","authors":"Septimiu Crivei, Robert Pop","doi":"10.1142/s0219498825501348","DOIUrl":"https://doi.org/10.1142/s0219498825501348","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135869136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1142/s0219498825501038
Fang Du, Hao Wang
For an [Formula: see text]-local vertex operator algebra [Formula: see text], where [Formula: see text] is a simple vertex operator algebra, and [Formula: see text] is the group algebra of a finite subgroup of [Formula: see text], Frobenius reciprocity is investigated. We give an explicit construction and classification of admissible [Formula: see text]-modules in terms of admissible [Formula: see text]-modules. We also give a complete set of irreducible inequivalent admissible [Formula: see text]-modules.
{"title":"Classification of irreducible admissible modules for <i>S</i>-local vertex operator algebra <i>V</i>#<i>H</i>","authors":"Fang Du, Hao Wang","doi":"10.1142/s0219498825501038","DOIUrl":"https://doi.org/10.1142/s0219498825501038","url":null,"abstract":"For an [Formula: see text]-local vertex operator algebra [Formula: see text], where [Formula: see text] is a simple vertex operator algebra, and [Formula: see text] is the group algebra of a finite subgroup of [Formula: see text], Frobenius reciprocity is investigated. We give an explicit construction and classification of admissible [Formula: see text]-modules in terms of admissible [Formula: see text]-modules. We also give a complete set of irreducible inequivalent admissible [Formula: see text]-modules.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1142/s0219498825500884
M. H. Bien, P. T. Nhan, N. H. T. Nhat
Let [Formula: see text] be a local ring with maximal ideal [Formula: see text], let [Formula: see text] be a natural number greater than [Formula: see text] and let [Formula: see text] be a matrix in the general linear group [Formula: see text] of degree [Formula: see text] over [Formula: see text]. We firstly show that if the matrix [Formula: see text] is nonscalar in [Formula: see text] and [Formula: see text] are invertible elements in [Formula: see text], then there exists an invertible element [Formula: see text] such that [Formula: see text] is similar to the product [Formula: see text] in which [Formula: see text] is a lower uni-triangular matrix and [Formula: see text] is an upper triangular matrix whose diagonal entries are [Formula: see text]. We then present some applications of this factorization to find decompositions of matrices in [Formula: see text] into product of commutators and involutions.
{"title":"Some Certain Decompositions of Matrices Over Local Rings","authors":"M. H. Bien, P. T. Nhan, N. H. T. Nhat","doi":"10.1142/s0219498825500884","DOIUrl":"https://doi.org/10.1142/s0219498825500884","url":null,"abstract":"Let [Formula: see text] be a local ring with maximal ideal [Formula: see text], let [Formula: see text] be a natural number greater than [Formula: see text] and let [Formula: see text] be a matrix in the general linear group [Formula: see text] of degree [Formula: see text] over [Formula: see text]. We firstly show that if the matrix [Formula: see text] is nonscalar in [Formula: see text] and [Formula: see text] are invertible elements in [Formula: see text], then there exists an invertible element [Formula: see text] such that [Formula: see text] is similar to the product [Formula: see text] in which [Formula: see text] is a lower uni-triangular matrix and [Formula: see text] is an upper triangular matrix whose diagonal entries are [Formula: see text]. We then present some applications of this factorization to find decompositions of matrices in [Formula: see text] into product of commutators and involutions.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1142/s0219498825500963
J. Prabu, J. Mahalakshmi, S. Santhakumar
In this paper, we constructed a class of [Formula: see text]-weight linear codes over [Formula: see text] under the homogeneous weight metric by their generator matrices, where [Formula: see text] and [Formula: see text] The Gray images of some class of these codes over [Formula: see text] are [Formula: see text]-ary nonlinear codes, which have the same weight distributions as that of the two-weight [Formula: see text]-ary linear codes of type SU1 in the sense of [R. Calderbank and W. M. Kantor, The geometry of two-weight codes, Bull. London Math. Soc. 18(2) (1986) 97–122]. Also, we obtained the minimum distance of the dual codes of the constructed codes. Further, we discussed some optimal linear codes over [Formula: see text] with respect to Plotkin-type bound from the constructed codes when [Formula: see text] Furthermore, we investigated the applications in strongly regular graphs and secret sharing schemes.
{"title":"A class of <i>t</i>-weight codes and its applications","authors":"J. Prabu, J. Mahalakshmi, S. Santhakumar","doi":"10.1142/s0219498825500963","DOIUrl":"https://doi.org/10.1142/s0219498825500963","url":null,"abstract":"In this paper, we constructed a class of [Formula: see text]-weight linear codes over [Formula: see text] under the homogeneous weight metric by their generator matrices, where [Formula: see text] and [Formula: see text] The Gray images of some class of these codes over [Formula: see text] are [Formula: see text]-ary nonlinear codes, which have the same weight distributions as that of the two-weight [Formula: see text]-ary linear codes of type SU1 in the sense of [R. Calderbank and W. M. Kantor, The geometry of two-weight codes, Bull. London Math. Soc. 18(2) (1986) 97–122]. Also, we obtained the minimum distance of the dual codes of the constructed codes. Further, we discussed some optimal linear codes over [Formula: see text] with respect to Plotkin-type bound from the constructed codes when [Formula: see text] Furthermore, we investigated the applications in strongly regular graphs and secret sharing schemes.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1142/s0219498825300028
Luciano Maino, Marzio Mula, Federico Pintore
CSIDH is a post-quantum key-exchange scheme based on the action of ideal class groups on supersingular elliptic curves over prime fields. Its short keys and ciphertexts, together with its flexibility as a building block to construct complex cryptographic primitives, has motivated significant research on the efficiency of CSIDH and its resistance against side-channel attacks. In this work, some cutting-edge results from recent contributions are reviewed in a unified treatment, focusing on the mathematical ideas lying behind them rather than on cryptographic and low-level implementation techniques. In particular, we first describe ways to speed up the class-group-action evaluation, which range from the use of different models of elliptic curves to working with different ideal class groups. We then survey some constant-time variants of CSIDH, that make the time and memory consumption during the computation of a public/shared key independent of the secret key. Finally, we examine the computation of the ideal class action when the structure of the ideal class group is known, which is the case for a specific set of CSIDH parameters.
{"title":"A Review of Mathematical and Computational Aspects of CSIDH Algorithms","authors":"Luciano Maino, Marzio Mula, Federico Pintore","doi":"10.1142/s0219498825300028","DOIUrl":"https://doi.org/10.1142/s0219498825300028","url":null,"abstract":"CSIDH is a post-quantum key-exchange scheme based on the action of ideal class groups on supersingular elliptic curves over prime fields. Its short keys and ciphertexts, together with its flexibility as a building block to construct complex cryptographic primitives, has motivated significant research on the efficiency of CSIDH and its resistance against side-channel attacks. In this work, some cutting-edge results from recent contributions are reviewed in a unified treatment, focusing on the mathematical ideas lying behind them rather than on cryptographic and low-level implementation techniques. In particular, we first describe ways to speed up the class-group-action evaluation, which range from the use of different models of elliptic curves to working with different ideal class groups. We then survey some constant-time variants of CSIDH, that make the time and memory consumption during the computation of a public/shared key independent of the secret key. Finally, we examine the computation of the ideal class action when the structure of the ideal class group is known, which is the case for a specific set of CSIDH parameters.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1142/s021949882550094x
Huihui Zheng, Linlin Liu
In this paper, firstly, we introduce the notion of matching Rota–Baxter modules, which generalizes the notions of matching Rota–Baxter algebras and Rota–Baxter modules, and give its characteristic and construction. Secondly, we give the relation between matching Rota–Baxter modules and other modules structure. Finally, we introduce the notion of matching [Formula: see text]-operators of associative algebras which also generalizes the notion of matching Rota–Baxter algebras and give the solution of polarized associative Yang–Baxter equation by using the matching [Formula: see text]-operators of associative algebras. In addition, we introduce the definitions of the compatible matching [Formula: see text]-operators of associative algebras, matching Nijenhui operators, and compatible matching dendriform algebras, and consider their connection.
{"title":"Matching Rota-Baxter modules and Matching 𝒪-operators of associative algebras","authors":"Huihui Zheng, Linlin Liu","doi":"10.1142/s021949882550094x","DOIUrl":"https://doi.org/10.1142/s021949882550094x","url":null,"abstract":"In this paper, firstly, we introduce the notion of matching Rota–Baxter modules, which generalizes the notions of matching Rota–Baxter algebras and Rota–Baxter modules, and give its characteristic and construction. Secondly, we give the relation between matching Rota–Baxter modules and other modules structure. Finally, we introduce the notion of matching [Formula: see text]-operators of associative algebras which also generalizes the notion of matching Rota–Baxter algebras and give the solution of polarized associative Yang–Baxter equation by using the matching [Formula: see text]-operators of associative algebras. In addition, we introduce the definitions of the compatible matching [Formula: see text]-operators of associative algebras, matching Nijenhui operators, and compatible matching dendriform algebras, and consider their connection.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-03DOI: 10.1142/s0219498825501336
Fernando Sancho De Salas
{"title":"Cohomology of Partially Ordered Sets and Ext's","authors":"Fernando Sancho De Salas","doi":"10.1142/s0219498825501336","DOIUrl":"https://doi.org/10.1142/s0219498825501336","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135869151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-02DOI: 10.1142/s021949882550063x
Markus Grassl, Anna-Lena Horlemann, Violetta Weger
We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric quantum codes. We set up the theoretic framework for this weight and metric, including upper and lower bounds, asymptotic behavior of random codes, and we show the existence of an optimal family of codes achieving the Singleton-type upper bound.
{"title":"The Subfield Metric and its Application to Quantum Error Correction","authors":"Markus Grassl, Anna-Lena Horlemann, Violetta Weger","doi":"10.1142/s021949882550063x","DOIUrl":"https://doi.org/10.1142/s021949882550063x","url":null,"abstract":"We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric quantum codes. We set up the theoretic framework for this weight and metric, including upper and lower bounds, asymptotic behavior of random codes, and we show the existence of an optimal family of codes achieving the Singleton-type upper bound.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135874433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-01DOI: 10.1142/s021949882550080x
Chris Monico
In [D. R. L. Brown, Plactic key agreement (insecure?), J. Math. Cryptol. 17(1) (2023) 20220010], a novel cryptographic key exchange technique was proposed using the plactic monoid, based on the apparent difficulty of solving division problems in that monoid. Specifically, given elements [Formula: see text] in the plactic monoid, the problem is to find [Formula: see text] for which [Formula: see text], given that such a [Formula: see text] exists. In this paper, we introduce a metric on the plactic monoid and use it to give a probabilistic algorithm for solving that problem which is fast for parameter values in the range of interest.
在[D。R. L. Brown, Plactic key agreement (insecure?)， J. Math。Cryptol. 17(1)(2023) 20220010]，基于求解plactic单群中除法问题的明显困难，提出了一种新的加密密钥交换技术。具体地说，给定plactic monooid中的元素[Formula: see text]，问题是找到[Formula: see text]的[Formula: see text]，假设存在这样一个[Formula: see text]。在本文中，我们引入了一个关于plactic monooid的度量，并利用它给出了一个求解该问题的概率算法，该算法对于参数值在感兴趣的范围内是快速的。
{"title":"Division in the Plactic Monoid","authors":"Chris Monico","doi":"10.1142/s021949882550080x","DOIUrl":"https://doi.org/10.1142/s021949882550080x","url":null,"abstract":"In [D. R. L. Brown, Plactic key agreement (insecure?), J. Math. Cryptol. 17(1) (2023) 20220010], a novel cryptographic key exchange technique was proposed using the plactic monoid, based on the apparent difficulty of solving division problems in that monoid. Specifically, given elements [Formula: see text] in the plactic monoid, the problem is to find [Formula: see text] for which [Formula: see text], given that such a [Formula: see text] exists. In this paper, we introduce a metric on the plactic monoid and use it to give a probabilistic algorithm for solving that problem which is fast for parameter values in the range of interest.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135011744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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