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Applicable Algebra in Engineering, Communication and Computing OnlineFirst articles

27.02.2024 | Original Paper

Optimal constacyclic codes with minimum distance four

Let $$n=2(p^m-1)/(p-1)$$ n = 2 ( p m - 1 ) / ( p - 1 ) , where p is an odd prime and $$m>1$$ 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 $$[n,n-2m,4]$$ [ n …

verfasst von:
Yajing Zhou, Xiaoshan Kai, Zhonghua Sun

25.02.2024 | Original Paper

On differential spectra of involutions with low differential uniformity over finite fields with even characteristic

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 …

verfasst von:
Guoqiang Liu, Sha Jiang, Kangquan Li

Open Access 09.02.2024 | Original Paper

Weighted product of point clouds and simplicial complexes

This paper extends the concept of weighted point clouds and weighted simplicial complexes by introducing product point clouds and product simplicial complexes within a commutative ring with unity. Within an integral domain, the introduction of a …

verfasst von:
Archana Babu, Sunil Jacob John, Baiju Thankachan

04.02.2024 | Original Paper

Weight hierarchies of a class of three-weight p-ary linear codes from inhomogeneous quadratic functions

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 …

verfasst von:
Shupeng Hu, Fei Li, Xiumei Li

19.01.2024 | Original Paper

Linear complementary pairs of constacyclic n-D codes over a finite commutative ring

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 …

verfasst von:
Ridhima Thakral, Sucheta Dutt, Ranjeet Sehmi

18.01.2024 | Original Paper

On the classification of non-exceptional APN functions

An almost perfect non-linear (APN) function over $$\mathbb {F}_{2^n}$$ F 2 n is called exceptional APN if it remains APN over infinitely many extensions of $$\mathbb {F}_{2^n}$$ F 2 n . Exceptional APN functions have attracted attention of many …

verfasst von:
Nurdagül Anbar, Tekgül Kalaycı, Nihal Yurdakul

07.01.2024 | Original Paper

Low-rank parity-check codes over finite commutative rings

Low-Rank Parity-Check (LRPC) codes are a class of rank metric codes that have many applications specifically in network coding and cryptography. Recently, LRPC codes have been extended to Galois rings which are a specific case of finite rings. In …

verfasst von:
Hermann Tchatchiem Kamche, Hervé Talé Kalachi, Franck Rivel Kamwa Djomou, Emmanuel Fouotsa

30.12.2023 | Original Paper

Spectral analysis for signed social networks

In complex real-world networks, the relation among vertices (people) changes over time. Even with millions of vertices, adding new vertices or deleting a few previous ones can drastically change the network’s dynamics. The Iterated Local …

verfasst von:
Anita Kumari Rao, Bableen Kaur, Sachin Somra, Deepa Sinha

27.12.2023 | Original Paper

A class of BCH codes with length

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 $$\frac{q^{2m}-1}{q+1}$$ q 2 m - 1 q + 1 over the finite fields …

verfasst von:
Binbin Pang, Xiaoshan Kai, Jun Gao

16.12.2023 | Original Paper

Construction of a class of at most three-weight linear codes and the applications

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 …

verfasst von:
Wenhui Liu, Xiaoni Du, Xingbin Qiao

07.12.2023 | Original Paper

Several classes of optimal cyclic codes with three zeros

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 …

verfasst von:
Tingting Wu, Li Liu, Lanqiang Li

16.11.2023 | Original Paper

A special scalar multiplication algorithm on Jacobi quartic curves

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 …

verfasst von:
Jiang Weng, Aiwang Chen, Tao Huang, Weifeng Ji

02.11.2023 | Original Paper

Using elliptic curves to construct 3D arrays

We present a new method of constructing three dimensional periodic arrays by composing a two dimensional periodic array with a sequence of shifts consisting of a cyclic group of points on an elliptic curve over a prime field $${\mathbb {F}}_p$$ F …

verfasst von:
Alcibíades Bustillo-Zárate, Dorothy Bollman, José Ortiz-Ubarri

25.10.2023 | Original Paper

Frames over finite fields and self-dual codes

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 …

verfasst von:
Minjia Shi, Yingying Liu, Jon-Lark Kim, Patrick Solé

21.10.2023 | Original Paper

Further results on the -differential uniformity of some functions over finite fields with odd characteristic

Functions with low differential uniformity have wide applications in cryptography. In this paper, by using the quadratic character of $${\mathbb {F}}_{p^n}^*$$ F p n ∗ , we further investigate the $$(-1)$$ ( - 1 ) -differential uniformity of these …

verfasst von:
Qian Liu, Ximeng Liu, Meixiang Chen, Jian Zou, Zhiwei Huang

20.10.2023 | Original Paper

MDS codes based on orthogonality of quasigroups

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 …

verfasst von:
Satish Kumar, Harshdeep Singh, Indivar Gupta, Ashok Ji Gupta

04.10.2023 | Original Paper

Batch point compression in the context of advanced pairing-based protocols

This paper continues previous ones about compression of points on elliptic curves $$E_b\!: y^2 = x^3 + b$$ E b : y 2 = x 3 + b (with j-invariant 0) over a finite field $$\mathbb {F}_{\!q}$$ F q of characteristic $$p > 3$$ p > 3 . It is shown in …

verfasst von:
Dmitrii Koshelev

04.10.2023 | Original Paper

Nonlinear complexity from the Hermitian and the Suzuki function fields

The notion of $$k-$$ 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 $$(q-1)(q^{2}-1)$$ ( q - 1 ) ( q 2 - 1 ) with high …

verfasst von:
Ferruh Özbudak, Nesrin Tutaş

26.09.2023 | Original Paper

Representing piecewise linear functions by functions with small arity

A piecewise linear function can be described in different forms: as a nested expression of $$\min$$ min - and $$\max$$ max -functions, as a difference of two convex piecewise linear functions, or as a linear combination of maxima of affine-linear …

verfasst von:
Christoph Koutschan, Bernhard Moser, Anton Ponomarchuk, Josef Schicho

24.09.2023 | Original Paper

Fuchsian holonomic sequences

Many sequences that arise in combinatorics and the analysis of algorithms turn out to be holonomic (note that some authors prefer the terminology D-finite). In this paper, we study various basic algorithmic problems for such sequences $$(f_n)_{n …

verfasst von:
Joris van der Hoeven