Let R be a commutative ring with identity and A(R) be the set of ideals with non-zero annihilator. The annihilator-ideal graph of R is defined as the graph $$\mathrm{A_I}(R)$$ A I ( R ) with the vertex set $$A(R)^*=A(R)\setminus \{0\}$$ A ( R ) ∗ …

Let C be a two and three-weight ternary code. Furthermore, we assume that $$C_\ell $$ C ℓ are t-designs for all $$\ell $$ ℓ by the Assmus–Mattson theorem. We show that $$t \le 5$$ t ≤ 5 . As a corollary, we provide a new characterization of the …

In this paper we use the puncturing and shortening techniques on two already-known classes of optimal cyclic codes in order to obtain three new classes of optimal linear codes achieving the Griesmer bound. The weight distributions for these codes …

The investigation of partially APN functions has attracted a lot of research interest recently. In this paper, we present several new infinite classes of 0-APN power functions over $$\mathbb {F}_{2^n}$$ F 2 n by using the multivariate method and …

In this paper, we consider the finite groups $$\begin{aligned} H_{(t,l,m)}=\langle a,b,c | a^t=b^l=c^m=1, [a,b]=c, [a,c]=[b,c]=1\rangle . \end{aligned}$$ H ( t , l , m ) = ⟨ a , b , c | a t = b l = c m = 1 , [ a , b ] = c , [ a , c ] = [ b , c ] = …

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 $$\rho$$ ρ -Walsh–Hadamard …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …