Related papers: Cyclic relative difference families with block siz…
Circular external difference families (CEDFs) are a recently-introduced variation of external difference families with applications to non-malleable threshold schemes: a $(v,m,\ell,1)$-CEDF is an $m$-sequence $(A_0, \ldots, A_{m-1})$ of…
A cycle with four blocks $C(k_{1}, k_{2},k_{3},k_{4})$ is an oriented cycle formed of four blocks of lengths $k_{1}, k_{2}, k_{3}$ and $k_{4}$ respectively. Recently, Cohen et al. conjectured that for every positive integers $k_{1}, k_{2},…
In this paper, a family of reducible cyclic codes over GF(p) whose duals have four zeros is presented, where p is an odd prime. Furthermore, the weight distribution of these cyclic codes is determined.
A cycle C(k1,k2,...,kn) is the oriented cycle formed of n blocks of lengths k1,k2,...,kn-1 and kn respectively. In 2018 Cohen et al. conjectured that for every positive integers k1,k2,...,kn there exists a constant g(k1,k2,...,kn) such that…
Subspace codes have recently been used for error correction in random network coding. In this work, we focus on one-orbit cyclic subspace codes. If $S$ is an $\mathbb{F}_q$-subspace of $\mathbb{F}_{q^n}$, then the one-orbit cyclic subspace…
Strong difference families of special types are introduced to produce new relative difference families from the point of view of both asymptotic existences and concrete examples. As applications, group divisible designs of type $30^u$ with…
In this paper we discuss the existence problem for a semi-cyclic holey group divisible design of type (n,m^t) with block size 3, which is denoted by a 3-SCHGDD of type (n,m^t). When n=3, a 3-SCHGDD of type (3,m^t) is equivalent to a…
Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
We consider the existence problem for a semi-cyclic holey group divisible design of type (n,m^t) with block size 3, which is denoted by a 3-SCHGDD of type (n,m^t). When t is odd and n\neq 8 or t is doubly even and t\neq 8, the existence…
We construct many new cyclic (v;r,s;lambda) difference families with v less than or equal 50. In particular we construct the difference families with parameters (45;18,10;9), (45;22,22;21), (47;21,12;12), (47;19,15;12), (47;22,14;14),…
In this paper, we construct a new family of distance-optimal binary cyclic codes with the minimum distance $6$ and a new family of distance-optimal quaternary cyclic codes with the minimum distance $4$. We also construct several families of…
Cyclic codes are an important subclass of linear codes with wide applications in communication systems and data storage systems. In 2013, Ding and Helleseth presented nine open problems on optimal ternary cyclic codes $\mathcal{C}_{(1,e)}$.…
Let $G$ be a finite group and $\cF$ be a family of subgroups of $G$ closed under conjugation and taking subgroups. We consider the question whether there exists a periodic relative $\cF$-projective resolution for $\bbZ$ when $\cF$ is the…
We construct several cyclic $(v;k_1,k_2,k_3;\lambda)$ difference families with $v\equiv3 \pmod{4}$ a prime and $\lambda=k_1+k_2+k_3-(3v-1)/4$. Such families can be used in conjunction with the well-known Paley-Todd difference sets to…
In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In this paper, we settle an open problem…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let $m=2\ell+1$ for an integer $\ell\geq 1$…
(Strong) circular external difference families (which we denote as CEDFs and SCEDFs) can be used to construct nonmalleable threshold schemes. They are a variation of (strong) external difference families, which have been extensively studied…
A four blocks cycle C(k1,k2,k3,k4) is an oriented cycle formed by the union of four internally disjoint directed paths of lengths k1,k2,k3 and k4 respectively. El Mniny proved that if D is a digraph having a spanning out-tree T with no…
Let $m\geq 3$ be an odd integer and $p$ be an odd prime. % with $p-1=2^rh$, where $h$ is an odd integer. In this paper, many classes of three-weight cyclic codes over $\mathbb{F}_{p}$ are presented via an examination of the condition for…