相关论文: The weight distributions of two classes of p ary c…

For an odd prime $p$ and two positive integers $n\geq 3$ and $k$ with $\frac{n}{{\rm gcd}(n,k)}$ being odd, the paper determines the weight distribution of a $p$-ary cyclic code $\mathcal{C}$ over $\mathbb{F}_{p}$ with nonzeros…

In this paper, a family of six-weight cyclic codes over GF(p) whose duals have two zeros is presented, where p is an odd prime. And the weight distribution of these cyclic codes is determined.

Because of efficient encoding and decoding algorithms, cyclic codes are an important family of linear block codes, and have applications in communica- tion and storage systems. However, their weight distributions are known only for a few…

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, a family of $p$-ary cyclic…

In this paper, a family of cyclic codes over $\mathbb{F}_{p}$ whose duals have five zeros is presented, where $p$ is an odd prime. Furthermore, the weight distributions of these cyclic codes are determined.

Cyclic codes are a subclass of linear codes and have wide applications in consumer electronics, data storage systems, and communication systems due to their efficient encoding and decoding algorithms. Cyclic codes with many zeros and their…

Cyclic codes have been widely used in digital communication systems and consume electronics as they have efficient encoding and decoding algorithms. The weight distribution of cyclic codes has been an important topic of study for many…

Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three zeros. Recently, \cite{Y-X-D12}…

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, a class of three-weight…

Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. Most previous results obtained so far were for cyclic codes with no more than three zeroes. Inspired by the works…

Let m, k be positive integers, p be an odd prime and $\pi $ be a primitive element of $\mathbb{F}_{p^m}$. In this paper, we determine the weight distribution of a family of cyclic codes $\mathcal{C}_t$ over $\mathbb{F}_p$, whose duals have…

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.

In this paper, for an even integer $n\geq 4$ and any positive integer $k$ with ${\rm gcd}(n/2,k)={\rm gcd}(n/2-k,2k)=d$ being odd, a class of $p$-ary codes $\mathcal{C}^k$ is defined and their weight distribution is completely determined,…

Cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes, have been studied for many years. However, the weight distributions of cyclic codes are difficult to determine. From…

Let $m$, $k$ be positive integers such that $\frac{m}{\gcd(m,k)}\geq 3$, $p$ be an odd prime and $\pi $ be a primitive element of $\mathbb{F}_{p^m}$. Let $h_1(x)$ and $h_2(x)$ be the minimal polynomials of $-\pi^{-1}$ and…

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Cyclic codes have been studied for many years, but their weight…

Cyclic codes have attracted a lot of research interest for decades. In this paper, for an odd prime $p$, we propose a general strategy to compute the complete weight enumerator of cyclic codes via the value distribution of the corresponding…

Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let $p\ge 5$ be an odd prime and $m$ be…

Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, we determined the complete weight enumerator of two classes of p-ary linear codes constructed from defining set.…

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…