Pub Date : 2023-05-19DOI: 10.1007/s00200-023-00608-4
Tim Alderson, Benjamin Morine
A combinatorial problem concerning the maximum size of the (Hamming) weight set of an $$[n,k]_q$$ linear code was recently introduced. Codes attaining the established upper bound are the Maximum Weight Spectrum (MWS) codes. Those $$[n,k]_q$$ codes with the same weight set as $$mathbb {F}_q^n$$ are called Full Weight Spectrum (FWS) codes. FWS codes are necessarily “short”, whereas MWS codes are necessarily “long”. For fixed k, q the values of n for which an $$[n,k]_q$$ -FWS code exists are completely determined, but the determination of the minimum length M(H, k, q) of an $$[n,k]_q$$ -MWS code remains an open problem. The current work broadens discussion first to general coordinate-wise weight functions, and then specifically to the Lee weight and a Manhattan like weight. In the general case we provide bounds on n for which an FWS code exists, and bounds on n for which an MWS code exists. When specializing to the Lee or to the Manhattan setting we are able to completely determine the parameters of FWS codes. As with the Hamming case, we are able to provide an upper bound on $$M({mathscr {L}},k,q)$$ (the minimum length of Lee MWS codes), and pose the determination of $$M({mathscr {L}},k,q)$$ as an open problem. On the other hand, with respect to the Manhattan weight we completely determine the parameters of MWS codes.
{"title":"MWS and FWS codes for coordinate-wise weight functions","authors":"Tim Alderson, Benjamin Morine","doi":"10.1007/s00200-023-00608-4","DOIUrl":"https://doi.org/10.1007/s00200-023-00608-4","url":null,"abstract":"A combinatorial problem concerning the maximum size of the (Hamming) weight set of an $$[n,k]_q$$ linear code was recently introduced. Codes attaining the established upper bound are the Maximum Weight Spectrum (MWS) codes. Those $$[n,k]_q$$ codes with the same weight set as $$mathbb {F}_q^n$$ are called Full Weight Spectrum (FWS) codes. FWS codes are necessarily “short”, whereas MWS codes are necessarily “long”. For fixed k, q the values of n for which an $$[n,k]_q$$ -FWS code exists are completely determined, but the determination of the minimum length M(H, k, q) of an $$[n,k]_q$$ -MWS code remains an open problem. The current work broadens discussion first to general coordinate-wise weight functions, and then specifically to the Lee weight and a Manhattan like weight. In the general case we provide bounds on n for which an FWS code exists, and bounds on n for which an MWS code exists. When specializing to the Lee or to the Manhattan setting we are able to completely determine the parameters of FWS codes. As with the Hamming case, we are able to provide an upper bound on $$M({mathscr {L}},k,q)$$ (the minimum length of Lee MWS codes), and pose the determination of $$M({mathscr {L}},k,q)$$ as an open problem. On the other hand, with respect to the Manhattan weight we completely determine the parameters of MWS codes.","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135576353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-17DOI: 10.1007/s00200-023-00609-3
Boran Kim
{"title":"Correction: Determination for minimum symbol-pair and RT weights via torsional degrees of repeated-root cyclic codes","authors":"Boran Kim","doi":"10.1007/s00200-023-00609-3","DOIUrl":"10.1007/s00200-023-00609-3","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"35 4","pages":"589 - 589"},"PeriodicalIF":0.6,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135861225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-13DOI: 10.1007/s00200-023-00606-6
H. Zantema, Vincent van Oostrom
{"title":"The paint pot problem and common multiples in monoids","authors":"H. Zantema, Vincent van Oostrom","doi":"10.1007/s00200-023-00606-6","DOIUrl":"https://doi.org/10.1007/s00200-023-00606-6","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48208169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-13DOI: 10.1007/s00200-023-00604-8
Y. Liu, X. Cao, Zhengbang Zha
{"title":"More classes of optimal quinary cyclic codes of form $${mathcal {C}}_{(1,e,s)}$$","authors":"Y. Liu, X. Cao, Zhengbang Zha","doi":"10.1007/s00200-023-00604-8","DOIUrl":"https://doi.org/10.1007/s00200-023-00604-8","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45582324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-09DOI: 10.1007/s00200-023-00607-5
Marcin Choiński
In this paper we introduce and analyze a discrete SIS epidemic model for a homogeneous population. As a discretization method the strictly positive scheme was chosen. The presented model is built from its continuous counterpart known from literature. We firstly present basic properties of the system. Later we discuss local stability of stationary states and global stability for the disease-free stationary state. The results for this state are expressed with the use of the basic reproduction number. The main conclusion from our work is that conditions for stability of the stationary states do not depend on the step size of the discretization method. This fact stays in contrary to other discrete models analyzed in our previous papers. Theoretical results are accomplished with numerical simulations.
{"title":"A discrete SIS-model built on the strictly positive scheme","authors":"Marcin Choiński","doi":"10.1007/s00200-023-00607-5","DOIUrl":"10.1007/s00200-023-00607-5","url":null,"abstract":"<div><p>In this paper we introduce and analyze a discrete <i>SIS</i> epidemic model for a homogeneous population. As a discretization method the strictly positive scheme was chosen. The presented model is built from its continuous counterpart known from literature. We firstly present basic properties of the system. Later we discuss local stability of stationary states and global stability for the disease-free stationary state. The results for this state are expressed with the use of the basic reproduction number. The main conclusion from our work is that conditions for stability of the stationary states do not depend on the step size of the discretization method. This fact stays in contrary to other discrete models analyzed in our previous papers. Theoretical results are accomplished with numerical simulations.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"35 2022","pages":"17 - 30"},"PeriodicalIF":0.6,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-023-00607-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45166937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-04DOI: 10.1007/s00200-023-00602-w
Marco Cianfriglia, Elia Onofri, Silvia Onofri, M. Pedicini
{"title":"Fourteen years of cube attacks","authors":"Marco Cianfriglia, Elia Onofri, Silvia Onofri, M. Pedicini","doi":"10.1007/s00200-023-00602-w","DOIUrl":"https://doi.org/10.1007/s00200-023-00602-w","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45636548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-26DOI: 10.1007/s00200-023-00605-7
Boran Kim
There are various metrics for researching error-correcting codes. Especially, high-density data storage system gives the existence of inconsistency for the reading and writing process. The symbol-pair metric is motivated for outputs that have overlapping pairs of symbols in a certain channel. The Rosenbloom–Tsfasman (RT) metric is introduced since there exists a problem that is related to transmission over several parallel communication channels with some channels not available for the transmission. In this paper, we determine the minimum symbol-pair weight and RT weight of repeated-root cyclic codes over (mathfrak R=mathbb {F}_{p^m}[u]/langle u^4rangle ) of length (n=p^k). For the determination, we explicitly present third torsional degree for all different types of cyclic codes over (mathfrak R) of length n.
{"title":"Determination for minimum symbol-pair and RT weights via torsional degrees of repeated-root cyclic codes","authors":"Boran Kim","doi":"10.1007/s00200-023-00605-7","DOIUrl":"10.1007/s00200-023-00605-7","url":null,"abstract":"<div><p>There are various metrics for researching error-correcting codes. Especially, high-density data storage system gives the existence of inconsistency for the reading and writing process. The symbol-pair metric is motivated for outputs that have overlapping pairs of symbols in a certain channel. The Rosenbloom–Tsfasman (RT) metric is introduced since there exists a problem that is related to transmission over several parallel communication channels with some channels not available for the transmission. In this paper, we determine the minimum symbol-pair weight and RT weight of repeated-root cyclic codes over <span>(mathfrak R=mathbb {F}_{p^m}[u]/langle u^4rangle )</span> of length <span>(n=p^k)</span>. For the determination, we explicitly present third torsional degree for all different types of cyclic codes over <span>(mathfrak R)</span> of length <i>n</i>.</p></div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"35 4","pages":"573 - 588"},"PeriodicalIF":0.6,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42822754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-22DOI: 10.1007/s00200-023-00601-x
M. Pazoki, R. Nikandish
{"title":"Computing the (forcing) strong metric dimension in strongly annihilating-ideal graphs","authors":"M. Pazoki, R. Nikandish","doi":"10.1007/s00200-023-00601-x","DOIUrl":"https://doi.org/10.1007/s00200-023-00601-x","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42668152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-02-21DOI: 10.1007/s00200-023-00597-4
Marlene Koelbing, Bernhard Garn, Enrico Iurlano, I. Kotsireas, D. Simos
{"title":"Algebraic and SAT models for SCA generation","authors":"Marlene Koelbing, Bernhard Garn, Enrico Iurlano, I. Kotsireas, D. Simos","doi":"10.1007/s00200-023-00597-4","DOIUrl":"https://doi.org/10.1007/s00200-023-00597-4","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48363389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"x-superoptimal pairings on elliptic curves with odd prime embedding degrees: BW13-P310 and BW19-P286","authors":"Emmanuel Fouotsa, Laurian Azebaze Guimagang, Raoul Ayissi","doi":"10.1007/s00200-023-00596-5","DOIUrl":"https://doi.org/10.1007/s00200-023-00596-5","url":null,"abstract":"","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"1 1","pages":"1-19"},"PeriodicalIF":0.7,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48519380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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