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New characterizations of generalized Boolean functions Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2024-03-11 Zhiyao Yang, Pinhui Ke, Zuling Chang
This paper focuses on providing the characteristics of generalized Boolean functions from a new perspective. We first generalize the classical Fourier transform and correlation spectrum into what we will call the \(\rho\)-Walsh–Hadamard transform (\(\rho\)-WHT) and the \(\rho\)-correlation spectrum, respectively. Then a direct relationship between the \(\rho\)-correlation spectrum and the \(\rho\)-WHT
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The 4-adic complexity of quaternary sequences with optimal odd-periodic autocorrelation magnitude Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2024-03-04 Xiaoyan Jing, Zhefeng Xu
Based on the inverse Gray mapping and sign alternation transform, a new family of quaternary sequences with optimal odd-periodic autocorrelation magnitude has been constructed by using the Legendre sequence pair, twin-prime sequence pair and GMW sequence pair. In this paper, we use the correlation properties of the Legendre sequence pair, twin-prime sequence pair and GMW sequence pair to determine
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Optimal constacyclic codes with minimum distance four Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2024-02-27 Yajing Zhou, Xiaoshan Kai, Zhonghua Sun
Let \(n=2(p^m-1)/(p-1)\), where p is an odd prime and \(m>1\) is a positive integer. In this paper, we research optimal p-ary constacyclic codes with two zeros. Two classes of optimal p-ary \([n,n-2m,4]\) constacyclic codes are presented by searching the solutions of certain congruence equations over \(\mathbb {F}_{p^m}\). Four explicit constructions of optimal constacyclic codes with such parameters
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On differential spectra of involutions with low differential uniformity over finite fields with even characteristic Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2024-02-25 Guoqiang Liu, Sha Jiang, Kangquan Li
In this paper, we determine the differential spectra of two known classes of involutions with low differential uniformity over finite fields with even characteristic completely. The key point of our method is that we propose several new definitions called special and ordinary points. In addition, it is interesting that one of our differential spectra is relative to the well-known Kloosterman sum.
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Weighted product of point clouds and simplicial complexes Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2024-02-09 Archana Babu, Sunil Jacob John, Baiju Thankachan
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Weight hierarchies of a class of three-weight p-ary linear codes from inhomogeneous quadratic functions Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2024-02-04 Shupeng Hu, Fei Li, Xiumei Li
The weight hierarchy of a linear code have been an important research topic in coding theory since Wei’s original work in 1991. In this paper, choosing \(D=\Big \{(x,y)\in \Big ({\mathbb {F}}_{p^{s_1}}\times {\mathbb {F}}_{p^{s_2}}\Big )\Big \backslash \{(0,0)\}: f(x)+\text {Tr}_1^{s_2}(\alpha y)=0\Big \}\) as a defining set, where \(\alpha \in {\mathbb {F}}_{p^{s_2}}^*\), f(x) is a quadratic form
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Linear complementary pairs of constacyclic n-D codes over a finite commutative ring Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2024-01-19 Ridhima Thakral, Sucheta Dutt, Ranjeet Sehmi
In this paper, a necessary condition which is sufficient as well for a pair of constacyclic 2-D codes over a finite commutative ring R to be an LCP of codes has been obtained. Also, a characterization of non-trivial LCP of constacyclic 2-D codes over R has been given and total number of such codes has been determined. The above results on constacyclic 2-D codes have been extended to constacyclic 3-D
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On the classification of non-exceptional APN functions Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2024-01-18 Nurdagül Anbar, Tekgül Kalaycı, Nihal Yurdakul
An almost perfect non-linear (APN) function over \(\mathbb {F}_{2^n}\) is called exceptional APN if it remains APN over infinitely many extensions of \(\mathbb {F}_{2^n}\). Exceptional APN functions have attracted attention of many researchers in the last decades. While the classification of exceptional APN monomials has been done by Hernando and McGuire, it has been conjectured by Aubry, McGuire and
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Low-rank parity-check codes over finite commutative rings Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2024-01-07 Hermann Tchatchiem Kamche, Hervé Talé Kalachi, Franck Rivel Kamwa Djomou, Emmanuel Fouotsa
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Spectral analysis for signed social networks Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-12-30 Anita Kumari Rao, Bableen Kaur, Sachin Somra, Deepa Sinha
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A class of BCH codes with length $$\frac{q^{2m}-1}{q+1}$$ Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-12-27
Abstract As an important class of cyclic codes, BCH codes are widely employed in satellite communications, DVDs, CD, DAT etc. In this paper, we determine the dimension of BCH codes of length \(\frac{q^{2m}-1}{q+1}\) over the finite fields \({\mathbb {F}}_q\) . We settle a conjecture about the largest q-cyclotomic coset leader modulo n which was proposed by Wu et al. We also get the second largest q-cyclotomic
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Construction of a class of at most three-weight linear codes and the applications Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-12-16 Wenhui Liu, Xiaoni Du, Xingbin Qiao
Linear codes are widely studied due to their important applications in authentication codes, association schemes and strongly regular graphs, etc. In this paper, a class of at most three-weight linear codes is constructed by selecting a new defining set, then the parameters and weight distributions of codes are determined by exponential sums. Results show that almost all the linear codes we constructed
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Several classes of optimal cyclic codes with three zeros Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-12-07 Tingting Wu, Li Liu, Lanqiang Li
As a class of linear codes, cyclic codes are widely used in communication systems, consumer electronics and data storage systems due to their favorable properties. In this paper, we construct two classes of optimal p-ary cyclic codes with parameters \([p^m-1, p^m-\frac{3m}{2}-2, 4]\) by analyzing the solutions of certain polynomials over finite fields. Furthermore, we propose an efficient method to
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A special scalar multiplication algorithm on Jacobi quartic curves Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-11-16 Jiang Weng, Aiwang Chen, Tao Huang, Weifeng Ji
At present, GLV/GLS scalar multiplication mainly focuses on elliptic curves in Weierstrass form, attempting to find and construct more and more efficiently computable endomorphism. In this paper, we investigate the application of the GLV/GLS scalar multiplication technique to Jacobi Quartic curves. Firstly, we present a concrete construction of efficiently computable endomorphisms for this type of
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Using elliptic curves to construct 3D arrays Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-11-02 Alcibíades Bustillo-Zárate, Dorothy Bollman, José Ortiz-Ubarri
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Generalized characteristic sets and new multivariate difference dimension polynomials Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-10-28 Alexander Levin
We introduce a new type of characteristic sets of difference polynomials using a generalization of the concept of effective order to the case of partial difference polynomials and a partition of the basic set of translations \(\sigma\). Using properties of these characteristic sets, we prove the existence and outline a method of computation of a multivariate dimension polynomial of a finitely generated
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Frames over finite fields and self-dual codes Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-10-25 Minjia Shi, Yingying Liu, Jon-Lark Kim, Patrick Solé
Modular strongly regular graphs have been introduced by Greaves et al. (Linear Algebra Appl 639:50–80, 2022). We show that a related class of isodual codes is asymptotically good. Equiangular tight frames over finite fields also introduced by the same authors in 2022 are shown here to connect with self-dual codes. We give several examples of equiangular tight frames over finite fields arising from
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MDS codes based on orthogonality of quasigroups Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-10-20 Satish Kumar, Harshdeep Singh, Indivar Gupta, Ashok Ji Gupta
In this paper, we propose a novel method for constructing maximum distance separable (MDS) codes based on the extended invertibility and orthogonality of quasigroups. We provide various methods of constructing an orthogonal system of k-ary operations over \(Q^2\) using a special type of k-ary operations over Q, where Q is any arbitrary finite set. Then we use concepts of strong orthogonality of k-ary
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Further results on the $$(-1)$$ -differential uniformity of some functions over finite fields with odd characteristic Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-10-21 Qian Liu, Ximeng Liu, Meixiang Chen, Jian Zou, Zhiwei Huang
Functions with low differential uniformity have wide applications in cryptography. In this paper, by using the quadratic character of \({\mathbb {F}}_{p^n}^*\), we further investigate the \((-1)\)-differential uniformity of these functions in odd characteristic: (1) \(f_1(x)=x^d\), where \(d=-\frac{p^n-1}{2}+p^k+1\), n and k are two positive integers satisfying \(\frac{n}{\gcd (n,k)}\) is odd; (2)
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Batch point compression in the context of advanced pairing-based protocols Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-10-04 Dmitrii Koshelev
This paper continues previous ones about compression of points on elliptic curves \(E_b\!: y^2 = x^3 + b\) (with j-invariant 0) over a finite field \(\mathbb {F}_{\!q}\) of characteristic \(p > 3\). It is shown in detail how any two (resp., three) points from \(E_b(\mathbb {F}_{\!q})\) can be quickly compressed to two (resp., three) elements of \(\mathbb {F}_{\!q}\) (apart from a few auxiliary bits)
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Nonlinear complexity from the Hermitian and the Suzuki function fields Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-10-04 Ferruh Özbudak, Nesrin Tutaş
The notion of \(k-\)th order nonlinear complexity has been studied from various aspects. Geil, Özbudak and Ruano (Semigroup Forum 98:543–555, 2019) gave a construction of a sequence of length \((q-1)(q^{2}-1)\) with high nonlinear complexity by using the Weierstrass semigroup of two distinct rational points on a Hermitian function field over \(F_{q^{2}}\), and they improved the bounds on the \(k-\)th
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Representing piecewise linear functions by functions with small arity Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-09-26 Christoph Koutschan, Bernhard Moser, Anton Ponomarchuk, Josef Schicho
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Fuchsian holonomic sequences Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-09-24 Joris van der Hoeven
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The 4-adic complexity of new quaternary sequences with good autocorrelation Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-09-21 Yan Wang, Jiawei Li, Nian Li, Yanxi Fu
Quaternary sequences with high 4-adic complexity have attracted widespread attention in communication and cryptography systems. In this paper, for an odd prime p, several new classes of quaternary sequences with even period 2p are constructed by using the Legendre sequences of period p. And the autocorrelation distribution of the new quaternary sequences is derived. We determine the 4-adic complexity
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Perfect codes in proper intersection power graphs of finite groups Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-09-21 Xuanlong Ma, Lan Li, Guo Zhong
Given a finite group G with the identity e, the proper intersection power graph of G is the graph with vertex set \(G\setminus \{e\}\), in which two distinct vertices x and y are adjacent if \(\langle x\rangle \cap \langle y\rangle \) is non-trivial. In this paper, we give a necessary and sufficient condition for a proper intersection power graph to contain a perfect code. As applications, we classify
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Array-designed reversible and complementary codes over GF(4) Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-09-19 Manabu Hagiwara, Whan-Hyuk Choi, Jon-Lark Kim
Array-designed codes are capable of correcting row and column deletions. In this paper, we introduce array-designed reversible and complementary codes over the finite field GF(4), which can correct row deletions and column deletions errors. Hence our codes can be useful for DNA codes. We also propose a construction method of array-designed reversible and complementary codes. As examples, we describe
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Exploring implications of Trace (Inversion) formula and Artin algebras in extremal combinatorics Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-08-13 Luis M. Pardo
This note is just a modest contribution to prove several classical results in Combinatorics from notions of Duality in some Artinian K-algebras (mainly through the Trace Formula), where K is a perfect field of characteristics not equal to 2. We prove how several classic combinatorial results are particular instances of a Trace (Inversion) Formula in finite \(\mathbb {Q}\)-algebras. This is the case
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Three new classes of optimal quinary cyclic codes with minimum distance four Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-08-07 Yan Liu, Xiwang Cao
Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an important subject of study for many years. Recently, several classes of optimal quinary cyclic codes of the forms \(\mathcal {C}_{(0,1,e)}\) and \(\mathcal {C}_{(1,e,s)}\) are presented in the literature, where \(s=\frac{5^m-1}{2}\) and \(2 \le e \le 5^{m}-2\). In this paper
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Generic Gröbner basis of a parametric ideal and its application to a comprehensive Gröbner system Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-08-03 Katsusuke Nabeshima
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Linear label code of a root lattice using Gröbner bases Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-07-28 Malihe Aliasgari, Daniel Panario, Mohammad-Reza Sadeghi
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Dihedral codes with 1-dimensional hulls and 1-dimensional linear complementary pairs of dihedral codes Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-07-19 S. T. Dougherty, Serap Şahinkaya, Deniz Ustun
In this paper, we study dihedral codes with 1-dimensional hulls and we determine precisely when dihedral codes over finite fields with 1-dimensional hulls exist. Moreover, we show that these codes come canonically in pairs. We also introduce 1-dimensional linear complementary pairs of dihedral codes and examine the properties of this class of codes. As an application, we obtain 1-dimensional linear
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Constructing doubly even self-dual codes and even unimodular lattices from Hadamard matrices Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-07-14 Dean Crnković, Andrea Švob
We show that from every skew-type Hadamard matrix of order 4t one can obtain a series of skew-type Hadamard matrices of order \(2^{i+2}t\), i a positive integer, whose binary linear codes are doubly even self-dual binary codes of length \(2^{i+2}t\). It is known that a doubly even self-dual binary code yields an even unimodular lattice. Hence, this construction of skew-type Hadamard matrices gives
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A note on a standard model for Galois rings Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-06-22 E. Martínez-Moro, A. Piñera-Nicolás, I. F. Rúa
In this work we present a standard model for Galois rings based on the standard model of their residual fields, that is, a a sequence of Galois rings starting with \({\mathbb Z}_{p^r}\) that coves all the Galois rings with that characteristic ring and such that there is an algorithm producing each member of the sequence whose input is the size of the required ring.
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Frobenius pseudo-variety of numerical semigroups with a given multiplicity and ratio Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-06-08 M. A. Moreno-Frías, J. C. Rosales
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On the higher-order nonlinearity of a new class of biquadratic Maiorana–McFarland type bent functions Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-05-31 Kezia Saini, Manish Garg
In 1974, Dillon introduced two significant classes of bent functions, namely the Maiorana–McFarland class and the Partial Spread class. In this article, we studied a new subclass of biquadratic Maiorana–McFarland type bent functions and presented a lower bound on the third-order nonlinearity of this class. The resulting lower bounds are better than the ones from the earlier bounds of Carlet (for all
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Explicit constructions of some infinite families of finite-dimensional irreducible representations of the type $${\textsf {E}}_{6}$$ and $${\textsf {E}}_{7}$$ simple Lie algebras Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-05-26 Robert G. Donnelly, Molly W. Dunkum, Austin White
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MWS and FWS codes for coordinate-wise weight functions Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-05-19 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
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The paint pot problem and common multiples in monoids Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-05-13 Hans Zantema, Vincent van Oostrom
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More classes of optimal quinary cyclic codes of form $${\mathcal {C}}_{(1,e,s)}$$ Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-05-13 Yan Liu, Xiwang Cao, Zhengbang Zha
Cyclic codes are an important subclass of linear codes. In this paper, we investigate the construction of quinary cyclic codes with parameters \([5^{m}-1, 5^{m}-2m-2, 4]\) and eight new classes optimal quinary cyclic codes of form \({\mathcal {C}}_{(1,e,s)}\) are presented by discussing the solutions of certain equations over \({\mathbb {F}}_{5^{m}}\).
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A discrete SIS-model built on the strictly positive scheme Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-05-09 Marcin Choiński
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Fourteen years of cube attacks Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-05-04 Marco Cianfriglia, Elia Onofri, Silvia Onofri, Marco Pedicini
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Determination for minimum symbol-pair and RT weights via torsional degrees of repeated-root cyclic codes Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-04-26 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
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Computing the (forcing) strong metric dimension in strongly annihilating-ideal graphs Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-04-22 M. Pazoki, R. Nikandish
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Using algebraic geometry to reconstruct a darboux cyclide from a calibrated camera picture Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-03-07 E. Hoxhaj, J. M. Menjanahary, J. Schicho
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The Legendre pseudorandom function as a multivariate quadratic cryptosystem: security and applications Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-03-01 István András Seres, Máté Horváth, Péter Burcsi
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Algebraic and SAT models for SCA generation Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-02-21 Marlene Koelbing, Bernhard Garn, Enrico Iurlano, Ilias S. Kotsireas, Dimitris E. Simos
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x-superoptimal pairings on elliptic curves with odd prime embedding degrees: BW13-P310 and BW19-P286 Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-02-16 Emmanuel Fouotsa, Laurian Azebaze Guimagang, Raoul Ayissi
The choice of the elliptic curve for a given pairing based protocol is primordial. For many cryptosystems based on pairings such as group signatures and their variants (EPID, anonymous attestation, etc) or accumulators, operations in the first pairing group \(\mathbb {G}\) of points of the elliptic curve is more predominant. At 128-bit security level two curves BW13-P310 and BW19-P286 with odd embedding
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On the 2-adic complexity of cyclotomic binary sequences of order four Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-02-13 Fuqing Sun, Qin Yue, Xia Li
Let \(p\equiv 1\pmod 4\) be a prime. In this paper, we support a new method, i.e., a product of 2-adic values for four binary sequences, to determine the maximum evaluations of the 2-adic complexity in all almost balanced cyclotomic binary sequences of order four with period \(N=p\), which are viewed as generalizing the results in Hu (IEEE Trans. Inf. Theory 60:5803–5804, 2014) and Xiong et al. (IEEE
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Two dimensional double cyclic codes over finite fields Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-02-01 Niloufar Hajiaghajanpour, Kazem Khashyarmanesh
A linear code C of length \(n = ru + sv\) is a two-dimensional \({\mathbb {F}}\)-double cyclic code if the set of coordinates can be partitioned into two arrays, such that any cyclic row-shifts and column-shifts of both arrays of a codeword is also a codeword. In this paper, we examine the algebraic structure of these codes and their dual codes in general. Moreover, we are interested in finding out
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Algorithmic counting of nonequivalent compact Huffman codes Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-01-12 Christian Elsholtz, Clemens Heuberger, Daniel Krenn
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The automorphism group of projective norm graphs Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-01-10 Tomas Bayer, Tamás Mészáros, Lajos Rónyai, Tibor Szabó
The projective norm graphs are central objects to extremal combinatorics. They appear in a variety of contexts, most importantly they provide tight constructions for the Turán number of complete bipartite graphs \(K_{t,s}\) with \(s>(t-1)!\). In this note we deepen their understanding further by determining their automorphism group.
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Bounds on the maximum nonlinearity of permutations on the rings $${\mathbb {Z}}_p$$ and $${\mathbb {Z}}_{2p}$$ Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2023-01-04 Prachi Gupta, P. R. Mishra, Atul Gaur
In 2016, Y. Kumar et al. in the paper ‘Affine equivalence and non-linearity of permutations over \({\mathbb {Z}}_n\)’ conjectured that: For \(n\ge 3\), the nonlinearity of any permutation on \({\mathbb {Z}}_n\), the ring of integers modulo n, cannot exceed \(n-2\). For an odd prime p, we settle the above conjecture when \(n=2p\) and for \(p\equiv 3 \pmod {4}\) we prove the above conjecture with an
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Quaternary Hermitian self-dual codes of lengths 26, 32, 36, 38 and 40 from modifications of well-known circulant constructions Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2022-12-22 Adam Michael Roberts
In this work, we give three new techniques for constructing Hermitian self-dual codes over commutative Frobenius rings with a non-trivial involutory automorphism using \(\lambda\)-circulant matrices. The new constructions are derived as modifications of various well-known circulant constructions of self-dual codes. Applying these constructions together with the building-up construction, we construct
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On a special type of permutation rational functions Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2022-12-16 Nurdagül Anbar
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Absorbing homogeneous polynomials arising from rational homotopy theory and graph theory Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2022-12-14 Mahmoud Benkhalifa
An ideal \({{\mathcal {I}}}\) of \({\mathbb {Q}}[x_1,\dots ,x_n]\) is said to be m-absorbing if any monomial of total degree \(p>m\) belongs to \({{\mathcal {I}}}\) and if there is a monomial M of total degree m such that \(M\not \in {{\mathcal {I}}}.\) Inspired by the fundamental work of Lechuga and Murillo (Topology 39:89–94, 2000) who established a connection between graph theory and rational homotopy
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Efficient computation of Riemann–Roch spaces for plane curves with ordinary singularities Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2022-12-01 Simon Abelard, Alain Couvreur, Grégoire Lecerf
We revisit the seminal Brill–Noether algorithm for plane curves with ordinary singularities. Our new approach takes advantage of fast algorithms for polynomials and structured matrices. We design a new probabilistic algorithm of Las Vegas type that computes a Riemann–Roch space in expected sub-quadratic time.
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De Nugis Groebnerialium 6: Rump, Ufnarovski, Zacharias Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2022-11-07 Michela Ceria, Ferdinando Mora
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Degröbnerization: a political manifesto Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2022-11-05 Michela Ceria, Samuel Lundqvist, Teo Mora
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On the existence of r-primitive pairs $$(\alpha ,f(\alpha ))$$ in finite fields Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2022-11-01 Hanglong Zhang, Xiwang Cao
Let r be a divisor of \(q-1.\) An element \(\alpha \in {\mathbb {F}}_{q}\) is said to be r-primitive if ord\((\alpha )=\frac{q-1}{r}\). In this paper, we discuss the existence of r-primitive pairs \((\alpha , f(\alpha ))\) where \(\alpha \in {\mathbb {F}}_q\), f(x) is a general rational function of degree sum m (degree sum is the sum of the degrees of numerator and denominator of f(x)) and the denominator
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Cellular structure of the Pommaret-Seiler resolution for quasi-stable ideals Appl. Algebra Eng. Commun. Comput. (IF 0.7) Pub Date : 2022-10-13 Rodrigo Iglesias, Eduardo Sáenz-de-Cabezón