Applicable Algebra in Engineering Communication and Computing最新文献_第7页

Frobenius pseudo-variety of numerical semigroups with a given multiplicity and ratio 具有给定多重性和比率的数值半群的Frobenius伪变种

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-06-08 DOI: 10.1007/s00200-023-00610-w

M. A. Moreno-Frías, J. C. Rosales

引用次数: 0

On the higher-order nonlinearity of a new class of biquadratic Maiorana–McFarland type bent functions 关于一类新的双二次Maiorana–McFarland型弯曲函数的高阶非线性

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-31 DOI: 10.1007/s00200-023-00611-9

Kezia Saini, Manish Garg

引用次数: 0

Explicit constructions of some infinite families of finite-dimensional irreducible representations of the type ({textsf {E}}_{6}) and ({textsf {E}}_{7}) simple Lie algebras $$｛textsf｛E｝｝_｛6｝$$和$$｝textsf｛E}｝_

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-26 DOI: 10.1007/s00200-023-00603-9

Robert G. Donnelly, Molly W. Dunkum, Austin White

{"title":"Explicit constructions of some infinite families of finite-dimensional irreducible representations of the type ({textsf {E}}_{6}) and ({textsf {E}}_{7}) simple Lie algebras","authors":"Robert G. Donnelly, Molly W. Dunkum, Austin White","doi":"10.1007/s00200-023-00603-9","DOIUrl":"10.1007/s00200-023-00603-9","url":null,"abstract":"<div>We construct every finite-dimensional irreducible representation of the simple Lie algebra of type ({textsf {E}}_{7}) whose highest weight is a nonnegative integer multiple of the dominant minuscule weight associated with the type ({textsf {E}}_{7}) root system. As a consequence, we obtain constructions of each finite-dimensional irreducible representation of the simple Lie algebra of type ({textsf {E}}_{6}) whose highest weight is a nonnegative integer linear combination of the two dominant minuscule ({textsf {E}}_{6})-weights. Our constructions are explicit in the sense that, if the representing space is d-dimensional, then a weight basis is provided such that all entries of the (d times d) representing matrices of the Chevalley generators are obtained via explicit, non-recursive formulas. To effect this work, we introduce what we call ({textsf {E}}_{6})- and ({textsf {E}}_{7})-polyminuscule lattices that analogize certain lattices associated with the famous special linear Lie algebra representation constructions obtained by Gelfand and Tsetlin.</div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 3","pages":"387 - 413"},"PeriodicalIF":0.6,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48674091","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}

引用次数: 0

MWS and FWS codes for coordinate-wise weight functions 坐标加权函数的MWS和FWS代码

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-19 DOI: 10.1007/s00200-023-00608-4

Tim Alderson, Benjamin Morine

{"title":"MWS and FWS codes for coordinate-wise weight functions","authors":"Tim Alderson, Benjamin Morine","doi":"10.1007/s00200-023-00608-4","DOIUrl":"10.1007/s00200-023-00608-4","url":null,"abstract":"<div>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.</div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 2","pages":"367 - 385"},"PeriodicalIF":0.6,"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}

引用次数: 0

Correction: Determination for minimum symbol-pair and RT weights via torsional degrees of repeated-root cyclic codes 更正：通过重复根循环码的扭转度确定最小符号对和 RT 权重

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-17 DOI: 10.1007/s00200-023-00609-3

Boran Kim

引用次数: 0

The paint pot problem and common multiples in monoids 油漆罐问题和一元群的公倍数

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-13 DOI: 10.1007/s00200-023-00606-6

Hans Zantema, Vincent van Oostrom

引用次数: 0

More classes of optimal quinary cyclic codes of form ({mathcal {C}}_{(1,e,s)}) 更多类形式为$$｛mathcal｛C｝｝_｛（1，e，s）｝的最优五元循环码$$

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-13 DOI: 10.1007/s00200-023-00604-8

Yan Liu, Xiwang Cao, Zhengbang Zha

引用次数: 0

A discrete SIS-model built on the strictly positive scheme 基于严格正格式的离散SIS模型

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-09 DOI: 10.1007/s00200-023-00607-5

Marcin Choiński

引用次数: 0

Fourteen years of cube attacks 立方体攻击14年

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-05-04 DOI: 10.1007/s00200-023-00602-w

Marco Cianfriglia, Elia Onofri, Silvia Onofri, Marco Pedicini

{"title":"Fourteen years of cube attacks","authors":"Marco Cianfriglia, Elia Onofri, Silvia Onofri, Marco Pedicini","doi":"10.1007/s00200-023-00602-w","DOIUrl":"10.1007/s00200-023-00602-w","url":null,"abstract":"<div>Algebraic Cryptanalysis is a widely used technique that tackles the problem of breaking ciphers mainly relying on the ability to express a cryptosystem as a solvable polynomial system. Each output bit/word can be expressed as a polynomial equation in the cipher’s inputs—namely the key and the plaintext or the initialisation vector bits/words. A part of research in this area consists in finding suitable algebraic structures where polynomial systems can be effectively solved, e.g., by computing Gröbner bases. In 2009, Dinur and Shamir proposed the cube attack, a chosen plaintext algebraic cryptanalysis technique for the offline acquisition of an equivalent system by means of monomial reduction; interpolation on cubes in the space of variables enables retrieving a linear polynomial system, hence making it exploitable in the online phase to recover the secret key. Since its introduction, this attack has received both many criticisms and endorsements from the crypto community; this work aims at providing, under a unified notation, a complete state-of-the-art review of recent developments by categorising contributions in five classes. We conclude the work with an in-depth description of the kite attack framework, a cipher-independent tool that implements cube attacks on GPUs. Mickey2.0 is adopted as a showcase.</div>","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":"36 2","pages":"285 - 325"},"PeriodicalIF":0.6,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00200-023-00602-w.pdf","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":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Determination for minimum symbol-pair and RT weights via torsional degrees of repeated-root cyclic codes 通过重根循环码的扭转度确定最小符号对和RT权值

IF 0.6 4区工程技术

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-04-26 DOI: 10.1007/s00200-023-00605-7

Boran Kim

引用次数: 0