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Semilinear Transformations in Coding Theory: A New Technique in Code-Based Cryptography
[article]

2022
*
arXiv
*
pre-print

*To*be specific, we introduce the so-called

*semilinear*

*transformation*

*in*

*coding*

*theory*, which is defined through an 𝔽_q-linear automorphism of 𝔽_q^m, then apply them

*to*construct a public key encryption ... This paper presents a new technique for disturbing the algebraic structure of linear

*codes*

*in*

*code*-based

*cryptography*. ...

*Semilinear*

*transformations*

*In*this section, we first introduce the concept of

*semilinear*

*transformations*

*and*investigate

*their*properties when acting on linear

*codes*. ...

##
###
The Hardness of Code Equivalence over $\mathbb{F}_q$ and Its Application to Code-Based Cryptography
[chapter]

2013
*
Lecture Notes in Computer Science
*

*In*this paper, we review the hardness of

*code*equivalence over Fq due

*to*some recent negative results

*and*argue on the possible implications

*in*

*code*-based

*cryptography*. ...

*In*particular, we present an improved version of the three-pass identification scheme of Girault

*and*discuss on a connection between

*code*equivalence

*and*the hidden subgroup problem. ... This Programme is supported by the Marie Curie Co-funding of Regional, National

*and*International Programmes (COFUND) of the European Commission. ...

##
###
On (2n/3-1)-resilient (n,2)-functions
[article]

2019
*
arXiv
*
pre-print

We suggest constructions of such functions

arXiv:1902.00022v1
fatcat:wvnufop7wzbnpgculkhzb2umry
*and*corresponding partitions, show connections with Latin hypercubes*and*binary 1-perfect*codes*, characterize the non-full-rank*and*the reducible functions from ... the considered class,*and*discuss the possibility*to*make a complete characterization of the class. ... Multifold perfect*codes**In*this subsection, we discuss equitable partitions with the quotient matrix (8)*and**their*connections with perfect*codes*. ...##
###
LESS is More: Code-Based Signatures Without Syndromes
[chapter]

2020
*
Lecture Notes in Computer Science
*

Devising efficient

doi:10.1007/978-3-030-51938-4_3
fatcat:5hw4o4loifcyfcofwjmehpns5u
*and*secure signature schemes based on*coding**theory*is still considered a challenge by the cryptographic community. ...*In*this paper, we construct a signature scheme by exploring a new approach*to*the area. ...*Codes*that are contained*in**their*dual, i.e. C ⊆ C ⊥ , are called weakly self-dual,*and**codes*that are equal*to**their*dual, i.e. C = C ⊥ , are called simply self-dual. ...##
###
Book Review: Finite element methods: Fifty years of the Courant element

1996
*
Mathematics of Computation
*

Various

doi:10.1090/s0025-5718-96-00755-7
fatcat:cmmgtlmdtvelpey5ntju5iizo4
*applications*are also discussed*in*these papers, which include compressible flows, convection-diffusion problems, elasticity*and*viscoelasticity, the Helmholtz equation, Maxwell equations, Navier-Stokes ...*To*commemorate the fiftieth anniversary of the publication of this paper, a conference was held at the University of Jyväskylä, Finland*in*1993. ...*Transforms*related*to*the DFT, such as the Laplace*transform*, the z-*transform*, the Chebyshev*transform*,*and*the Hartley*transform*, are treated*in*Chapter 8. ...##
###
Fourier's Method of Linear Programming and Its Dual

1986
*
The American mathematical monthly
*

also 11G50, 37P30]
14G50

doi:10.2307/2322281
fatcat:yvhgyh2epbcwdoqdhuaopkcrue
*Applications**to**coding**theory**and**cryptography*[See also 94A60, 94B27, 94B40] 14G99 None of the above, but*in*this section 14Hxx Curves 14H05 Algebraic functions; function ... , economics 46N20*Applications**to*differential*and*integral equations 46N30*Applications**in*probability*theory**and*statistics 46N40*Applications**in*numerical analysis [See also 65Jxx] 46N50*Applications*... 82D80 Nanostructures*and*nanoparticles 82D99 None of the above, but*in*this section 83-XX RELATIVITY*AND*GRAVITATIONAL*THEORY*83-00 General reference works (handbooks, dictionaries, bibliographies, ...##
###
Reference list of indexed articles

1999
*
Theoretical Computer Science
*

Zalcstein, The complexity of Grigorchuk groups with

doi:10.1016/s0304-3975(98)00320-x
fatcat:bdgg2ekzdjahdo7g2gtwbdye6m
*application**to**cryptography*88 (1) (1991) 83-98 1643. S. Cho*and*D.T. ... Warmuth,*Applications*of scheduling*theory**to*formal language*theory*37 (2) (1985) 217-243 732. R. De Simone, Higher-level synchronizing devices*in*MEIJE-SCCS 37 (3) (1985) 245-267 733. A. ...##
###
Book report

2004
*
Computers and Mathematics with Applications
*

Bayesian Predictive Profiles with

doi:10.1016/j.camwa.2004.06.021
fatcat:vi5ps7eddza7hfba726v3epvtq
*Applications**to*Retail Transaction Data (Igor V. Padhraic Smyth). 169. ... Starting the Segmentation Gene Cascade*in*Insects (Urs Schmidt-Ott*and*Ernst A. Wimmer). 18. The Evolution of Nematode Development: How Cells*and*Genes Change*their*Function (Ralf J. ...##
###
Ring geometries, two-weight codes, and strongly regular graphs

2008
*
Designs, Codes and Cryptography
*

Here we extend this classical result

doi:10.1007/s10623-007-9136-8
fatcat:3i7b3d6zhrfwxbhywmmleadq6q
*to*the case of a ring-linear*code*with exactly two nonzero homogeneous weights*and*multisets of points*in*an associated projective ring geometry. ... It is known that a linear two-weight*code*C over a finite field F q corresponds both*to*a multiset*in*a projective space over F q that meets every hyperplane*in*either a or b points for some integers a ... Acknowledgement The authors feel indebted*to*the reviewers for a variety of remarks*and*corrections which helped*to*improve the quality of the published paper. ...##
###
Systematic encoders for generalized Gabidulin codes and the q-analogue of Cauchy matrices
[article]

2020
*
arXiv
*
pre-print

*In*addition, our results allow

*to*give a new efficient criterion

*to*verify whether a rank metric

*code*of dimension k

*and*length n is a generalized Gabidulin

*code*. ...

*In*particular, as an

*application*, we construct Gabidulin

*codes*whose generator matrix is the concatenation of an identity block

*and*a Toeplitz/Hankel matrix. ... Acknowledgement The author would like

*to*thank Eimear Byrne for useful comments on the structure of the work

*and*Martino Borello for suggesting

*to*point out Lemma 12. ...

##
###
On a Class of Meromorphic Functions Related to Cho-Kwon-Srivastava Operator

2012
*
ISRN Applied Mathematics
*

by means of an operator given by Ghanim

doi:10.5402/2012/272678
fatcat:kn3oeobqmzh7tgbpns35eeyy4u
*and*Darus,*in*U={z:0<|z|<1},*and*investigate a number of inclusion relationships of these classes. ... We introduce new classes, Σn,λ*,μ,k(α,β,ρ)*and*Σn,λμ,k(α,β,ρ), of meromorphic functions defined by means of the Hadamard product of Cho-Kwon-Srivastava operator,*and*we define here a similar*transformation*... Simonis, Some new results on optimal*codes*over F5,Designs,*Codes**and**Cryptography*, vol. 30, 2003, pp. 97-111. цитирана в:M. Araya, M. ...##
###
On the number of roots of some linearized polynomials
[article]

2020
*
arXiv
*
pre-print

Linearized polynomials appear

arXiv:1909.00802v2
fatcat:ljw7cmfwv5dnnfwsvbdcgf2ufa
*in*many different contexts, such as rank metric*codes*,*cryptography**and*linear sets,*and*the main issue regards the characterization of the number of roots from*their*coefficients ... Also, we characterize the number of roots of such polynomials directly from*their*coefficients, dealing with matrices which are much smaller than the relative Dickson matrices*and*the companion matrices ... Introduction Linearized polynomials over F q n are important objects*in*the*theory*of finite fields*and**in*finite geometry since they correspond*to*F q -linear*transformations*of the n-dimensional F q ...##
###
Computational learning theory

1992
*
Proceedings of the twenty-fourth annual ACM symposium on Theory of computing - STOC '92
*

Abe [1] proves that the class of

doi:10.1145/129712.129746
dblp:conf/stoc/Angluin92
fatcat:7aw3cnd745bellyhu7phywpul4
*semilinear*sets of di- mensions 1*and*2 with unary*coding*is PAC-learnable by means of an Occam algorithm. ... It is logical that*cryptography*(which tries*to*make unpredictable things ever easier*to*compute)*and*computational learning*theory*(which tries*to*make more powerful classes of concepts predictable) should ...##
###
Incorporation of Deep Neural Network Reinforcement Learning with Domain Knowledge
[article]

2021
*
arXiv
*
pre-print

This paper inspects expansive ways

arXiv:2107.14613v2
fatcat:cddkguo3gvcgxn6s67ca26ucii
*to*affect encode such information as sensible*and*mathematical limitations*and*portrays methods*and*results that came*to*a couple of subcategories under all of those ... Integrating space data is uniquely important*to*the development of Knowledge understanding model, as well as other fields that aid*in*understanding information by utilizing the human-machine interface ... Theorem*theories*are often extremely related*to*coaching of FFNN, as [16] broadly discuss. ...##
###
Tight sets and m-ovoids of generalised quadrangles

2009
*
Combinatorica
*

Geometric

doi:10.1007/s00493-009-2179-x
fatcat:3lv4kl6qafbfdemivsj73n6miq
*Codes**and*Hyperovals Anton Betten I will outline the*theory*of geometric*codes**and**their*relationship*to*the construction of hyperovals*in*Desarguesian projective planes of even order. ...*In*the distance 5 case these*codes**and**their*duals have been studied a great deal, as they appear*in*many places*and*disguisesfor instance,*cryptography*, multiuser communications, orthogonal geometry over ...
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