arXiv subjects

Qin Yue

Publications and source records attributed to Qin Yue.

25 records · Page 2Linked to original sources

arXiv2017

A construction of $q$-ary linear codes with two weights

Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of $q$-ary linear codes from trace and norm functions over finite fields. The weight distributions of the linear codes are determined in some cases based on Gauss sums. It is interesting that our construction can produce optimal or almost optimal codes. Furthermore, we show that our codes can be used to construct secret sharing schemes with interesting access structures and strongly regular graphs with new parameters.

cs.IT↗

arXiv2016

Evaluation of the Hamming weights of a class of linear codes based on Gauss sums

Linear codes with a few weights have been widely investigated in recent years. In this paper, we mainly use Gauss sums to represent the Hamming weights of a class of $q$-ary linear codes under some certain conditions, where $q$ is a power of a prime. The lower bound of its minimum Hamming distance is obtained. In some special cases, we evaluate the weight distributions of the linear codes by semi-primitive Gauss sums and obtain some one-weight, two-weight linear codes. It is quite interesting that we find new optimal codes achieving some bounds on linear codes. The linear codes in this paper can be used in secret sharing schemes, authentication codes and data storage systems.

cs.IT↗

arXiv2016

A class of $q$-ary linear codes derived from irreducible cyclic codes

Recently, linear codes with a few weights were widely investigated due to their applications in secret sharing schemes and authentication schemes. In this letter, we present a class of $q$-ary linear codes derived from irreducible cyclic codes with $q$ a prime power. We use Gauss sums to represent its Hamming weights and obtain the bounds of its minimum Hamming distance. In some cases, we explicitly determine its weight distributions which generalize some known results. It is quite interesting that many new codes obtained in this letter are optimal according to some bounds on linear codes.

cs.IT↗

arXiv2015

Several classes of cyclic codes with either optimal three weights or a few weights

Cyclic codes with a few weights are very useful in the design of frequency hopping sequences and the development of secret sharing schemes. In this paper, we mainly use Gauss sums to represent the Hamming weights of a general construction of cyclic codes. As applications, we obtain a class of optimal three-weight codes achieving the Griesmer bound, which generalizes a Vega's result in \cite{V1}, and several classes of cyclic codes with only a few weights, which solve the open problem in \cite{V1}.

cs.IT↗

arXiv2013

Weight distributions of cyclic codes with respect to pairwise coprime order elements

Let $\Bbb F_r$ be an extension of a finite field $\Bbb F_q$ with $r=q^m$. Let each $g_i$ be of order $n_i$ in $\Bbb F_r^*$ and $\gcd(n_i, n_j)=1$ for $1\leq i \neq j \leq u$. We define a cyclic code over $\Bbb F_q$ by $$\mathcal C_{(q, m, n_1,n_2, ..., n_u)}=\{c(a_1, a_2, ..., a_u) : a_1, a_2, ..., a_u \in \Bbb F_r\},$$ where $$c(a_1, a_2, ..., a_u)=({Tr}_{r/q}(\sum_{i=1}^ua_ig_i^0), ..., {Tr}_{r/q}(\sum_{i=1}^ua_ig_i^{n-1}))$$ and $n=n_1n_2... n_u$. In this paper, we present a method to compute the weights of $\mathcal C_{(q, m, n_1,n_2, ..., n_u)}$. Further, we determine the weight distributions of the cyclic codes $\mathcal C_{(q, m, n_1,n_2)}$ and $\mathcal C_{(q, m, n_1,n_2,1)}$.

cs.IT↗

arXiv2013

Weight distribution of two classes of cyclic codes with respect to two distinct order elements

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 distribution are known only for a few cases. In this paper, let $\Bbb F_r$ be an extension of a finite field $\Bbb F_q$ and $r=q^m$, we determine the weight distribution of the cyclic codes $\mathcal C=\{c(a, b): a, b \in \Bbb F_r\},$ $$c(a, b)=(\mbox {Tr}_{r/q}(ag_1^0+bg_2^0), \ldots, \mbox {Tr}_{r/q}(ag_1^{n-1}+bg_2^{n-1})), g_1, g_2\in \Bbb F_r,$$ in the following two cases: (1) $\ord(g_1)=n, n|r-1$ and $g_2=1$; (2) $\ord(g_1)=n$, $g_2=g_1^2$, $\ord(g_2)=\frac n 2$, $m=2$ and $\frac{2(r-1)}n|(q+1)$.

cs.IT↗

arXiv2009

Weight Distribution of A p-ary Cyclic Code

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 $α^{-1}$, $α^{-(p^k+1)}$ and $α^{-(p^{3k}+1)}$, where $α$ is a primitive element of $\mathbb{F}_{p^n}$

cs.IT↗