A Class of Six-weight Cyclic Codes and Their Weight Distribution

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.Comment: arXiv admin note: text overlap with arXiv:1302.0952, arXiv:1302.0569, arXiv:1301.4824 by other author

A class of cyclic codes whose dual have five zeros

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

Gold type codes of higher relative dimension

Some new Gold type codes of higher relative dimension are introduced. Their weight distribution is determined

The weight distribution of a family of p-ary cyclic codes

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 two zeros $\pi^{-t}$ and $-\pi^{-t}$, where $t$ satisfies $t\equiv \frac{p^k+1}{2}p^\tau \ ({\rm mod}\ \frac{p^m-1}{2})$ for some $\tau \in \{0,1,\cdots, m-1\}$.Comment: 15 page

A Class of Five-weight Cyclic Codes and Their Weight Distribution

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.Comment: arXiv admin note: substantial text overlap with arXiv:1311.3391, and text overlap with arXiv:1302.0952 by other author

Optimal cyclic codes with generalized Niho type zeroes and the weight distribution

In this paper we extend the works \cite{gegeng2,XLZD} further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions. It is interesting to note that many cyclic codes in the family are optimal and have only a few non-zero weights. Besides using similar ideas from \cite{gegeng2,XLZD}, we carry out some subtle manipulation of certain exponential sums

Kasami type codes of higher relative dimension

Some new Kasami type codes of higher relative dimension is introduced. Their weight distribution is determined.Comment: arXiv admin note: substantial text overlap with arXiv:1506.0149

A Class of Reducible Cyclic Codes and Their Weight Distribution

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.Comment: arXiv admin note: substantial text overlap with arXiv:1312.463

Infinite families of 22-designs from a class of cyclic codes with two non-zeros

Combinatorial $t$-designs have wide applications in coding theory, cryptography, communications and statistics. It is well known that the supports of all codewords with a fixed weight in a code may give a $t$-design. In this paper, we first determine the weight distribution of a class of linear codes derived from the dual of extended cyclic code with two non-zeros. We then obtain infinite families of $2$-designs and explicitly compute their parameters from the supports of all the codewords with a fixed weight in the codes. By simple counting argument, we obtain exponentially many $2$-designs.Comment: arXiv admin note: substantial text overlap with arXiv:1903.0745

A class of pp-ary cyclic codes and their weight enumerators

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 $\pi^{-\frac{p^k+1}{2}}$ over $\mathbb{F}_p$, respectively. In the case of odd $\frac{m}{\gcd(m,k)}$, when $k$ is even, $\gcd(m,k)$ is odd or when $\frac{k}{\gcd(m,k)}$ is odd, Zhou et~al. in \cite{zhou} obtained the weight distribution of a class of cyclic codes $\mathcal{C}$ over $\mathbb{F}_p$ with parity-check polynomial $h_1(x)h_2(x)$. In this paper, we further investigate this class of cyclic codes $\mathcal{C}$ over $\mathbb{F}_p$ in the rest case of odd $\frac{m}{\gcd(m,k)}$ and the case of even $\frac{m}{\gcd(m,k)}$. Moreover, we determine the weight distribution of cyclic codes $\mathcal{C}$.Comment: 22 page