相关论文: The Weight Enumerator of Three Families of Cyclic …
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…
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 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. 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 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 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…
The determination of weight distribution of cyclic codes involves evaluation of Gauss sums and exponential sums. Despite of some cases where a neat expression is available, the computation is generally rather complicated. In this note, we…
In this paper, a family of five-weight reducible cyclic codes is presented. Furthermore, the weight distribution of these cyclic codes is determined, which follows from the determination of value distributions of certain exponential sums.
As a subclass of linear codes, cyclic codes have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, five families of three-weight…
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 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 have attracted a lot of research interest for decades as they have efficient encoding and decoding algorithms. In this paper, for an odd prime $p$, the weight distributions of two classes of $p$-ary cyclic codes are completely…
An important family of codes for data storage systems, cryptography, consumer electronics, and network coding for error control in digital communications are the so-called cyclic codes. This kind of linear codes are also important due to…
The weight distribution and weight hierarchy of linear codes are two important research topics in coding theory. In this paper, by choosing proper defining sets from inhomogeneous quadratic functions over $\mathbb{F}_{q}^{2},$ we construct…
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…
Recently, there has been intensive research on the weight distributions of cyclic codes. In this paper, we compute the weight distributions of three classes of cyclic codes with Niho exponents. More specifically, we obtain two classes of…
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 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.
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…
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.