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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…
We study the distribution of the number of rational points in a family of curves over a finite field of characteristic 2. This distribution determines the coset weight distribution of a certain BCH code.
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.
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…
We discuss a class of binary cyclic codes and their dual codes. The minimum distance is determined using algebraic geometry, and an application of Weil's theorem. We relate the weights appearing in the dual codes to the number of rational…
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we provide a slightly different approach toward the general problem and use it to solve one more special…
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}…
We introduce a formula for determining the number of codewords of weight 2 in cyclic codes and provide results related to the count of codewords with weight 3. Additionally, we establish a recursive relationship for binary cyclic codes that…
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…
We consider cyclic codes $\mathcal{C}_\mathcal{L}$ associated to quadratic trace forms in $m$ variables $Q_R(x) = \operatorname{Tr}_{q^m/q}(xR(x))$ determined by a family $\mathcal{L}$ of $q$-linearized polynomials $R$ over…
The duals of cyclic codes with two zeros have been extensively studied, and their weight distributions have recently been evaluated in some cases. In this note, we determine the weight distribution of a certain new class of such codes by…
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 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…
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we solve one more special case. The problem of finding the weight distribution is transformed into a…
Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes has many applications such as on the type II wire-tap channel, dealing with…
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…
Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we use the method developed before to solve one more special case. We make extensive use of standard…
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 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…
In this article, we illustrate an algorithm for the computation of the weight distribution of CRC codes. The recursive structure of CRC codes will give us an iterative way to compute the weight distribution of their dual codes starting from…