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Jinquan Luo

Publications and source records attributed to Jinquan Luo.

At least 37 records · Page 2Linked to original sources
arXiv2021

The Differential Spectrum of the Power Mapping $x^{p^n-3}$

Let $n$ be a positive integer and $p$ a prime. The power mapping $x^{p^n-3}$ over $\mathbb{F}_{p^n}$ has desirable differential properties, and its differential spectra for $p=2,\,3$ have been determined. In this paper, for any odd prime $p$, by investigating certain quadratic character sums and some equations over $\mathbb{F}_{p^n}$, we determine the differential spectrum of $x^{p^n-3}$ with a unified approach. The obtained result shows that for any given odd prime $p$, the differential spectrum can be expressed explicitly in terms of $n$. Compared with previous results, a special elliptic curve over $\mathbb{F}_{p}$ plays an important role in our computation for the general case $p \ge 5$.

cs.IT↗
arXiv2021

New Galois Hulls of GRS Codes and Application to EAQECCs

Galois hulls of linear codes have important applications in quantum coding theory. In this paper, we construct some new classes of (extended) generalized Reed-Solomon (GRS) codes with Galois hulls of arbitrary dimensions. We also propose a general method on constructing GRS codes with Galois hulls of arbitrary dimensions from special Euclidean orthogonal GRS codes. Finally, we construct several new families of entanglement-assisted quantum error-correcting codes (EAQECCs) and MDS EAQECCs by utilizing the above results.

cs.IT↗
arXiv2020

MDS Symbol-Pair Codes from Repeated-Root Cyclic Codes

Symbol-pair codes are proposed to combat pair-errors in symbol-pair read channels. The minimum symbol-pair distance is of significance in determining the error-correcting capability of a symbol-pair code. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that such codes can achieve the Singleton bound. In this paper, two new classes of MDS symbol-pair codes are proposed utilizing repeated-root cyclic codes over finite fields with odd characteristic. Precisely, these codes poss minimum symbol-pair distance ten or twelve, which is bigger than all the known MDS symbol-pair codes from constacyclic codes.

cs.IT↗
arXiv2020

New Classes of Entanglement-assisted Quantum MDS Codes

In this paper, we produce two new classes of entanglement-assisted quantum MDS codes (EAQMDS codes) with length $n|q^2-1$ and $n|q^2+1$ via cyclic codes over finite fields of odd characteristic. Among our constructions there are many EAQMDS codes with new parameters which have never been reported. And some of them have great larger minimum distance than known results.

cs.IT↗
arXiv2020

Entanglement-assisted Quantum MDS Codes from generalized Reed-Solomon Codes

In this paper, we produce some new classes of entanglement-assisted quantum MDS codes(EAQMDS codes for short) via generalized Reed-Solomon codes over finite fields of odd characteristic. Among our constructions, there are many EAQMDS codes with new lengths which have never been reported. Moreover, some of them have larger minimum distance than known results.

cs.IT↗
arXiv2019

Symbol-pair Weight Distributions of Some Linear Codes

In this paper, we investigate the symbol-pair weight distributions of MDS codes and simplex codes over finite fields. Furthermore, the result shows that all the nonzero codewords of simplex codes have the same symbol $b$-weight and rearrangement entries of codewords in simplex code may induce different symbol-pair weight. In addition, the symbol $b$-weight distributions of variation simplex codes over certain finite fields are derived.

cs.IT↗
arXiv2019

On Euclidean Hulls of MDS Codes

In this paper, we propose a mechanism on the constructions of MDS codes with arbitrary dimensions of Euclidean hulls. Precisely, we construct (extended) generalized Reed-Solomon(GRS) codes with assigned dimensions of Euclidean hulls from self-orthogonal GRS codes. It turns out that our constructions are more general than previous works on Euclidean hulls of (extended) GRS codes.

cs.IT↗
arXiv2019

Constructions of MDS Self-dual Codes from Short length

Systematic constructions of MDS self-dual codes is widely concerned. In this paper, we consider the constructions of MDS Euclidean self-dual codes from short length. Indeed, the exact constructions of MDS Euclidean self-dual codes from short length ($n=3,4,5,6$) are given. In general, we construct more new of $q$-ary MDS Euclidean self-dual codes from MDS self-dual codes of known length via generalized Reed-Solomon (GRS for short) codes and extended GRS codes.

cs.IT↗
arXiv2019

New MDS Euclidean Self-orthogonal Codes

In this paper, a criterion of MDS Euclidean self-orthogonal codes is presented. New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square $q$, about $\frac{1}{8}\cdot q$ new MDS Euclidean (almost) self-dual codes over $\F_q$ can be produced. Moreover, we can construct about $\frac{1}{4}\cdot q$ new MDS Euclidean self-orthogonal codes with different even lengths $n$ with dimension $\frac{n}{2}-1$.

cs.IT↗
arXiv2019

New Quantum MDS Codes over Finite Fields

In this paper, we present three new classes of $q$-ary quantum MDS codes utilizing generalized Reed-Solomon codes satisfying Hermitian self-orthogonal property. Among our constructions, the minimum distance of some $q$-ary quantum MDS codes can be bigger than $\frac{q}{2}+1$. Comparing to previous known constructions, the lengths of codes in our constructions are more flexible.

cs.IT↗
arXiv2019

New MDS Self-dual Codes over Finite Fields of Odd Characteristic

In this paper, we produce new classes of MDS self-dual codes via (extended) generalized Reed-Solomon codes over finite fields of odd characteristic. Among our constructions, there are many MDS self-dual codes with new parameters which have never been reported. For odd prime power $q$ with $q$ square, the total number of lengths for MDS self-dual codes over $\mathbb{F}_q$ presented in this paper is much more than those in all the previous results.

cs.IT↗
arXiv2019

Correcting Codes for Asymmetric Single Magnitude Four Error

An error model with asymmetric single magnitude four error is considered. This paper is about constructions of codes correcting single error over $\mathbb{Z}_{2^{a}3^{b}r}$. Firstly, we reduce the construction of a maximal size $B_{1}[4](2^{a}3^{b}r)$ set for $a\geq4$ and $\gcd(r,6)=1$ to the construction of a maximal size $B_{1}[4](2^{a-3}3^{b}r)$ set. Further, we will show that maximal size $B_{1}[4](8\cdot3^{b}r)$ sets can be reduced to maximal size $B_{1}[4](3^{b}r)$ sets. Finally, we give a lower bounds of maximal size $B_{1}[4](2r)$ and $B_{1}[4](2\cdot3^{b}r)$ sets.

cs.IT↗
arXiv2019

New Perfect Nonlinear Functions and Their Semifields

In this paper, two new classes of perfect nonlinear functions over $\mathbb{F}_{p^{2m}}$ are proposed, where $p$ is an odd prime. Furthermore, we investigate the nucleus of the corresponding semifields of these functions and show that the semifields are not isotopic to all the known semifields. Particularly, the new perfect nonlinear functions are CCZ-inequivalent to other classes in general.

cs.IT↗
arXiv2019

New Perfect Nonlinear Functions over Finite Fields

In this paper we present a new class of perfect nonlinear %Dembowski-Ostrom polynomials over $\mathbb{F}_{p^{2k}}$ for any odd prime $p$. In addition, we show that the new perfect nonlinear functions are CCZ-inequivalent to all the previously known perfect nonlinear functions in general.

cs.IT↗
arXiv2019

Asymmetric Single Magnitude Four Error Correcting Codes

Limited magnitude asymmetric error model is well suited for flash memory. In this paper, we consider the construction of asymmetric codes correcting single error over $\mathbb{Z}_{2^{k}r}$ and which are based on so called $B_{1}[4](2^{k}r)$ set. In fact, we reduce the construction of a maximal size $B_{1}[4](2^{k}r)$ set for $k\geq3$ to the construction of a maximal size $B_{1}[4](2^{k-3}r)$ set. Finally, we give a explicit formula of a maximal size $B_{1}[4](4r)$ set and some lower bounds of a maximal size $B_{1}[4](2r)$ set. By computer searching up to $q\leq106$, we conjecture that those lower bounds are tight.

cs.IT↗
arXiv2018

Optimal Equi-difference Conflict-avoiding Codes

An equi-differece conflict-avoiding code $(CAC^{e})\ \mathcal{C}$ of length $n$ and weight $ω$ is a collection of $ω$-subsets (called codewords) which has the form $\{0,i,2i,\cdots,(ω-1)i\}$ of $\mathbb{Z}_{n}$ such that $Δ(c_{1})\capΔ(c_{2})=\emptyset$ holds for any $c_{1},\ c_{2}\in\mathcal{C}$, $c_{1}\neq c_{2}$ where $Δ(c)=\{j-i \ (\mbox{mod}\ n) \; | \; i,j\in c,i\neq j\}.$ A code $\mathcal{C}\in CAC^{e}s$ with maximum code size for given $n$ and $ω$ is called optimal and is said to be perfect if $\cup_{c\in \mathcal{C}}Δ(c)=\mathbb{Z}_{n}\backslash \{0\}.$ In this paper, we show how to combine a $\mathcal{C}_{1}\in CAC^{e}(q_{1},ω)$ and a $\mathcal{C}_{2}\in CAC^{e}(q_{2},ω)$ into a $\mathcal{C}\in CAC^{e}(q_{1}q_{2},ω)$ under certain conditions. One necessary condition for a $CAC^{e}$ of length $q_{1}q_{2}$ and weight $ω$ being optimal is given. We also consider explicit construction of perfect $\mathcal{C}\in CAC^{e}(p,ω)$ of odd prime $p$ and weight $ω\geq3$. Finally, for positive integer $k$ and prime $p\equiv1 \ (\mbox{mod}\ 4k)$, we consider explicit construction of quasi-perfect $\mathcal{C}\in CAC^{e}(2p,4k+1)$.

cs.IT↗
arXiv2018

Construction of MDS Self-dual Codes over Finite Fields

In this paper, we obtain some new results on the existence of MDS self-dual codes utilizing (extended) generalized Reed-Solomon codes over finite fields of odd characteristic. For some fixed $q$, our results can produce more classes of MDS self-dual codes than previous works.

cs.IT↗