Hengjia Wei

Hengjia Wei
Peng Cheng Laboratory

Doctor of Philosophy

About

54
Publications
1,747
Reads
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185
Citations
Additional affiliations
April 2019 - present
Ben-Gurion University of the Negev
Position
  • PostDoc Position
January 2016 - April 2019
Nanyang Technological University
Position
  • Research Associate
October 2014 - December 2015
Capital Normal University
Position
  • PostDoc Position
Education
September 2009 - June 2014
Zhejiang University
Field of study
  • Mathematics
September 2005 - June 2009
Donghua University
Field of study
  • Mathematics

Publications

Publications (54)
Preprint
Full-text available
Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error ball. We construct two classes of such perfect codes correcting a single burst of length $2$ for $(1,0)$-limit...
Article
Error-correcting codes over sets, with applications to DNA storage, are studied. The DNA-storage channel receives a set of sequences, and produces a corrupted version of the set, including sequence loss, symbol substitution, symbol insertion/deletion, and limited-magnitude errors in symbols. Various parameter regimes are studied. New bounds on code...
Article
We study whether an asymmetric limited-magnitude ball may tile Zn. This ball generalizes previously studied shapes: crosses, semi-crosses, and quasi-crosses. Such tilings act as perfect error-correcting codes in a channel which changes a transmitted integer vector in a bounded number of entries by limited-magnitude errors. A construction of lattice...
Preprint
Full-text available
Motivated by applications to DNA storage, we study reconstruction and list-reconstruction schemes for integer vectors that suffer from limited-magnitude errors. We characterize the asymptotic size of the intersection of error balls in relation to the code's minimum distance. We also devise efficient reconstruction algorithms for various limited-mag...
Preprint
Full-text available
We study generalized covering radii, a fundamental property of linear codes that characterizes the trade-off between storage, latency, and access in linear data-query protocols such as PIR. We prove lower and upper bounds on the generalized covering radii of Reed-Muller codes, as well as finding their exact value in certain extreme cases. With the...
Article
We construct integer error-correcting codes and covering codes for the limited-magnitude error channel with more than one error. The codes are lattices that pack or cover the space with the appropriate error ball. Some of the constructions attain an asymptotic packing/covering density that is constant. The results are obtained via various methods,...
Article
We study scalar-linear and vector-linear solutions of the generalized combination network. We derive new upper and lower bounds on the maximum number of nodes in the middle layer, depending on the network parameters and the alphabet size. These bounds improve and extend the parameter range of known bounds. Using these new bounds we present a lower...
Preprint
Error-correcting codes over sets, with applications to DNA storage, are studied. The DNA-storage channel receives a set of sequences, and produces a corrupted version of the set, including sequence loss, symbol substitution, symbol insertion/deletion, and limited-magnitude errors in symbols. Various parameter regimes are studied. New bounds on code...
Preprint
We study scalar-linear and vector-linear solutions of the generalized combination network. We derive new upper and lower bounds on the maximum number of nodes in the middle layer, depending on the network parameters and the alphabet size. These bounds improve and extend the parameter range of known bounds. Using these new bounds we present a lower...
Preprint
We study whether an asymmetric limited-magnitude ball may tile $\mathbb{Z}^n$. This ball generalizes previously studied shapes: crosses, semi-crosses, and quasi-crosses. Such tilings act as perfect error-correcting codes in a channel which changes a transmitted integer vector in a bounded number of entries by limited-magnitude errors. A constructio...
Preprint
We construct integer error-correcting codes and covering codes for the limited-magnitude error channel with more than one error. The codes are lattices that pack or cover the space with the appropriate error ball. Some of the constructions attain an asymptotic packing/covering density that is constant. The results are obtained via various methods,...
Article
To equip DNA-based data storage with random-access capabilities, Yazdi et al. (2018) prepended DNA strands with specially chosen address sequences called primers and provided certain design criteria for these primers. We provide explicit constructions of error-correcting codes that are suitable as primer addresses and equip these constructions wi...
Article
In a bus with n wires, each wire has two states, '0' or '1', representing one bit of information. Whenever the state transitions from '0' to '1', or '1' to '0', joule heating causes the temperature to rise, and high temperatures have adverse effects on on-chip bus performance. Recently, the class of low-power cooling (LPC) codes was proposed to con...
Preprint
We study scalar-linear and vector-linear solutions to the generalized combination network. We derive new upper and lower bounds on the maximum number of nodes in the middle layer, depending on the network parameters. These bounds improve and extend the parameter range of known bounds. Using these new bounds we present a general lower bound on the g...
Preprint
Full-text available
A robust positioning pattern is a large array that allows a mobile device to locate its position by reading a possibly corrupted small window around it. In this paper, we provide constructions of binary positioning patterns, equipped with efficient locating algorithms, that are robust to a constant number of errors and have redundancy within a cons...
Article
Permutation codes and multipermutation codes are widely studied due to various applications in information theory. Designing codes correcting deletion errors has been the main subject of works in the literature and to the best of our knowledge, there exist only optimal codes capable of correcting a single deletion in a permutation. In this paper, w...
Preprint
Full-text available
To equip DNA-based data storage with random-access capabilities, Yazdi et al. (2018) prepended DNA strands with specially chosen address sequences called primers and provided certain design criteria for these primers. We provide explicit constructions of error-correcting codes that are suitable as primer addresses and equip these constructions with...
Preprint
Full-text available
A class of low-power cooling (LPC) codes, to control simultaneously both the peak temperature and the average power consumption of interconnects, was introduced recently. An $(n,t,w)$-LPC code is a coding scheme over $n$ wires that (A) avoids state transitions on the $t$ hottest wires (cooling), and (B) limits the number of transitions to $w$ in ea...
Article
The class of geometric orthogonal codes (GOCs) were introduced by Doty and Winslow (2016) for more robust macrobonding in DNA origami. They observed that GOCs are closely related to optical orthogonal codes (OOCs). It is possible for GOCs to have size greater than OOCs of corresponding parameters due to slightly more relaxed constraints on correlat...
Article
Group divisible covering designs (GDCDs) were introduced by Heinrich and Yin as a natural generalization of both covering designs and group divisible designs. They have applications in software testing and universal data compression. The minimum number of blocks in a k-GDCD of type gu is a covering number denoted by C(k,gu). When k=3, the values of...
Article
A uniformly resolvable design (URD) is a resolvable design in which each parallel class contains blocks of only one block size k. Such a class is denoted k-pc and for a given k the number of k-pcs is denoted rk. The number of points of the URD is denoted by v. In the literature, the existence of URDs of block sizes k1 and k2 with {k1,k2}∈{{2,3},{2,...
Article
Full-text available
Partitioned difference families are an interesting class of discrete structures which can be used to derive optimal constant composition codes. There have been intensive researches on the construction of partitioned difference families. In this paper, we consider the combinatorial approach. We introduce a new combinatorial configuration named parti...
Article
The research on directed PBDs is motivated by the construction of t-deletion/insertion-correcting codes. Fuji-Hara, Miao, Wang, and Yin have determined the existence of directed PBDs with block sizes from the set and the set completely. In this paper, we consider the cases of . We settle almost completely for these cases, leaving finite values unde...
Article
Let $K=\{k_1,k_2,\ldots,k_r\}$ and $L=\{l_1,l_2,\ldots,l_s\}$ be disjoint subsets of $\{0,1,\ldots,p-1\}$, where $p$ is a prime and $A=\{A_1,A_2,\ldots,A_m\}$ be a family of subsets of $[n]$ such that $|A_i|\pmod{p}\in K$ for all $A_i\in A$ and $|A_i\cap A_j|\pmod{p}\in L$ for $i\ne j$. In 1991, Alon, Babai and Suzuki conjectured that if $n\geq s+\...
Article
Full-text available
Given a database, the private information retrieval (PIR) protocol allows a user to make queries to several servers and retrieve a certain item of the database via the feedbacks, without revealing the privacy of the specific item to any single server. Classical models of PIR protocols require that each server stores a whole copy of the database. Re...
Article
A uniformly resolvable design (URD) is a resolvable design in which each parallel class contains blocks of only one block size k. Such a class is denoted k-pc and for a given k the number of k-pcs is denoted rk. Let v denote the number of points of the URD. For the case of block sizes 3 and 4 (both existing), the necessary conditions imply that v ≡...
Article
Full-text available
The construction of group divisible designs (GDDs) is a basic problem in design theory. While there have been some methods concerning the constructions of uniform GDDs, the construction of nonuniform GDDs remains a challenging problem. In this paper, we present a new approach to the construction of nonuniform GDDs with group type and block size k....
Article
Full-text available
Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, the bounds of MCWCs and the constructions of optimal MCWCs are studied. Firstly, we derive three different types of upper bounds which improve the Johnson-type bounds given by Chee {\sl et al....
Article
A triple system is a collection of b blocks, each of size three, on a set of v points. It is j-balanced when every two j-sets of points appear in numbers of blocks that are as nearly equal as possible, and well balanced when it is j-balanced for each . Well-balanced systems arise in the minimization of variance in file availability in distributed f...
Article
Grooming uniform all-to-all traffic in optical (SONET) rings with grooming ratio C requires the determination of a decomposition of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is mi...
Article
Grooming uniform all-to-all traffic in optical (SONET) rings with grooming ratio C requires the determination of a decomposition of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is mi...
Article
The sizes of optimal constant-composition codes of weight three have been determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes played an important role in their constructions. In this paper, we study the problem of constructing optimal ternary constant-composition codes with Hamming weight four and minimum distance six. T...
Article
In this paper, we continue to investigate the existence of 55-GDDs, 4-frames and 4-RGDDs, which have been studied by numerous researchers in the past two decades due to their vital applications in the constructions for other types of designs. Much progress has been made for the existence problems of these designs, while the problems are still open....
Article
Constructing non-uniform designs has become a topic of considerable interest over the last two decades due to the vital role of such designs in the constructions for other types of designs. Ge, Rees and Shalaby started the investigation into the spectrum of non-uniform Kirkman frames of type $h^{u}m^{1}$ . They determined the spectrum for the cas...
Article
Non-uniform group divisible designs (GDDs) and non-uniform Kirkman frames are useful in the constructions for other types of designs. In this paper, we consider the existence problems for K1(3)K1(3)-GDDs of type gum1gum1 with K1(3)={k:k≡1mod3}K1(3)={k:k≡1mod3} and Kirkman frames of type hum1hum1. First, we determine completely the spectrum for unif...
Article
A G-design of order n is a decomposition of the complete graph on n vertices into edge-disjoint subgraphs isomorphic to G. Grooming uniform all-to-all traffic in optical ring networks with grooming ratio C requires the determination of graph decompositions of the complete graph on n vertices into subgraphs each having at most C edges. The drop cost...
Article
Complete reducible super-simple (CRSS) designs are closely related to \(q\)-ary constant weight codes. A \((v,k,\lambda )\)-CRSS design is just an optimal \((v,2(k-1),k)_{\lambda +1}\) code. In this paper, we mainly investigate the existence of a \((v,5,2)\)-CRSS design and show that such a design exists if and only if \(v\equiv 1,5\pmod {20}\) and...
Article
Nonuniform group divisible designs (GDDs) have been studied by numerous researchers for the past two decades due to their essential role in the constructions for other types of designs. In this paper, we investigate the existence problem of {4}-GDDs of type gum1 for g≡0mod6. First, we determine completely the spectrum of {4}-GDDs of types 18um1 and...
Article
Non-uniform group divisible designs have been studied by numerous researchers in the past two decades due to their vital applications in the constructions for other types of designs. Much progress has been made for the existence of -GDDs of type , especially when is even. The corresponding problem for block size three had been solved by Colbourn et...
Article
Perfect t-deletion-correcting codes of length over the alphabet of size , denoted by perfect , can have different number of codewords, because the balls of radius with respect to LevenshteAn distance may be of different sizes. Thus determining all possible sizes of a perfect -deletion-correcting code makes sense. When , -deletion-correcting codes a...
Article
Non-uniform group divisible designs are instrumental in the constructions for other types of designs. Most of the progress for the existence of {4}-GDDs of type gum1 is on the case when gu is even, where the existence for small g has played a key role. In order to determine the spectrum for {4}-GDDs of type gum1 with gu being odd, we continue to in...

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