# Wende Chen's research while affiliated with Chinese Academy of Sciences and other places

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## Publications (37)

In min-max systems, the cycle time plays an important role on analyzing the performance metric. In this work, we mainly investigate the performances of the min-max systems with cycle time assignment, which corresponding to the feedback problem in linear systems. It is achieved that the cycle time can be assigned disjointedly by an output feedback i...

Finite projective geometry method is effectively used to study the relative generalized Hamming weights of 4-dimensional linear codes, which are divided into 9 classes in order to get much more information about the relative generalized Hamming weights, and part of the relative generalized Hamming weights of a 4-dimensional linear code with a 1-dim...

The value function and finite projective geometry methods are effective tools to study support weights of subcodes. Some new
results about support weights of a kind of subcodes are found by using the concept of the value function and finite projective
geometry methods. The new results provide a way to construct a class of two-weight codes.

Code equivalence is a basic concept in coding theory. The well-known theorem by MacWilliams gives a sufficient condition for code equivalence. Recently the MacWilliams theorem has been generalized, by Fan, Liu and Puig, making use of the generalized Hamming weights (GHWs). In this paper, we will present a further generalization of the MacWilliams t...

The relative subcodes are closely related to the concept of the relative generalized Hamming weight. Using projective geometry
methods and the concept of the relative generalized Hamming weight, the authors prove a property of the relative subcodes
which substantially improves the existing result.
Key wordsProjective subspaces-relative subcodes-th...

The properties satisfied by the value function are given. These properties can be used to study the generalized Hamming weight
and the relative generalized Hamming weight of certain linear codes.

In this article, some properties of the relative generalized Hamming weight (RGHW) of linear codes and their subcodes are
developed with techniques in finite projective geometry. The relative generalized Hamming weights of almost all 4-dimensional
q-ary linear codes and their subcodes are determined.

A variety of problems in computer science, operations research, control theory, etc., can be modeled as non-linear and non-differentiable
max–min systems. This paper introduces the global optimization into such systems. The criteria for the existence and uniqueness
of the globally optimal solutions are established using the high matrix, optimal max...

We study the minimal realization of a low dimension SISO linear system in the max-algebra. We classify 3-rank periodic unit impulse response sequence {g<sub>i</sub>}<sub>0</sub> <sup>infin</sup> into four categories according to their characteristic equations, and discuss the necessary and sufficient conditions of the existence of 3D minimal realiz...

This paper investigates the non-blocking optimal control and scheduling problems of multi-entry and multi-outlet serial production lines with the finite serial buffers. We develop the state equation and the optimal control law of the production lines. We also carry out the system performance analysis using the matrix row-difference monotonic theory...

In supply chains, the phenomenon of bullwhip effect (the variance amplification of order quantities observed in supply chain) has received a considerable attention by both theoretical researchers and practitioners as it leads to tremendous losses and poor customer services. This paper introduces a new control engineering technique called delayed ge...

For nonlinear discrete event dynamic systems described by a min-max function, we show that the cycle time can be assigned disjointedly by a state feedback, if and only if the system is reachable. Further, a simple necessary and sufficient condition for that the cycle time can be assigned independently by a state feedback is given. Hence the difficu...

The maximum of g<sub>2</sub> - d<sub>2</sub> for linear [n,k,d;q] codes C is studied. Here d<sub>2</sub> is the smallest size of the support of a two-dimensional subcode of C and g<sub>2</sub> is the smallest size of the support of a two-dimensional subcode of C which contains a codeword of weight d. For codes of dimension 4 or more, upper and lowe...

A constant-composition code is a special constant-weight code under the restriction that each symbol should appear a given number of times in each codeword. In this correspondence, we give a lower bound for the maximum size of the q-ary constant-composition codes with minimum distance at least 3. This bound is asymptotically optimal and generalizes...

There are a large number of linear block codes satisfying the chain condition. Their weight hierarchies are called chain good and form an important group in classifying all possible weight hierarchies. In this paper, we present a series of new sufficient conditions to determine which kinds of sequences are chain good weight hierarchies. Our results...

The weight hierarchy of a linear [n, k; q] codeC overGF(q) is the sequence (d
1,d
2, …,d
k) whered
r is the size of the smallest support of anr-dimensional subcode ofC. An [n, k; q] code satisfies the chain condition if there exists subcodesD
1⊂D
2⊂…⊂D
k=C ofC such thatD
r has dimensionr and support of sized
r for allr. Further,C satisfies the almo...

In this paper, by using a new kind of geometric structures, we present some sufficient conditions to determine the weight hierarchies of linear codes satisfying the chain condition.

A constant composition code is a special constant weight code under the restriction that each symbol should appear a given number of times in each codeword. In this paper, we give an asymptotically optimal lower bound for the maximum size of the q-ary constant composition codes with minimum distance at least 3. In addition, a number of optimum cons...

The difference g2−d2 for a q-ary linear [n,3,d] code C is studied. Here d2 is the second generalized Hamming weight, that is, the smallest size of the support of a 2-dimensional subcode of C; and g2 is the second greedy weight, that is, the smallest size of the support of a 2-dimensional subcode of C which contains a codeword of weight d. For codes...

The weight hierarchy of a binary linear [n,k] code C is the sequence (d1,d2,…,dk) where dr is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes. The possible weight hierarchies in each class are given. For one class the details of the proofs are included.

From nonlinear discrete event dynamic systems with the applicable background of a large-scale digital integrated circuit,
a new conception of coloring graphs on the system is advanced, the necessary and sufficient condition of upper-level observability
is given, and the necessary and sufficient condition of respective reachability is simplified and...

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the
sequence (d<sub>1</sub>,d<sub>2</sub>,…,d<sub>k</sub>) where d
<sub>r</sub> is the smallest support of an r-dimensional subcode of C.
An [n,k;q] code is extremal non-chain if for any r and s, where
1⩽r<s⩽k, there are no subspaces D and E such that D ⊂ E,
dim D=r, dim E=s, w<s...

The difference g
2 - d2
for a binary linear [n,k,d] code C is studied. Here d2
is the smallest size of the support of a 2-dimensional subcode of C and g
2 is the smallest size of the support of a 2-dimensional subcode of C which contains a codeword of weight d. For codes of dimension 4, the maximal value of g
2-d2
is determined. For general dimensi...

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the
sequence (d<sub>1</sub>,d<sub>2</sub>,??????,d<sub>k
</sub>) where d<sub>r</sub> is the smallest support of an r-dimensional
subcode of C. An [n,k;q] code is extremal nonchain if, for any r and s,
where 1⩽r<s⩽k, there are no subspaces D and E such that
D???E, dim D=r, dim E=s...

New constructions of regular disjoint distinct difference sets (DDDS) are presented. In particular, multiplicative and additive DDDS are considered.

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the sequence (d1,d2,...,dk) where dr is the smallest support of an r–dimensional subcode of C. By explicit construction, it is shown that if a sequence (a1,a2,...,ak) satisfies certain conditions, then it is the weight hierarchy of a code satisfying the chain condition.

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the
sequence (d<sub>1</sub>,d<sub>2</sub>,…,d<sub>k</sub>) where d
<sub>r</sub> is the smallest support of an r-dimensional subcode of C.
The codes of dimension 4 are collected in classes. For each class bounds
and extremal codes are discussed

An (h, J)-distinct sum set is a set of J integers such that all sums of h elements (repetitions allowed) are distinct. An (h, I, J)-set of disjoint distinct sum sets is a set of I disjoint (h, J)-distinct sum sets with positive elements. A number of constructions of such sets are given.

. The weight hierarchy of a linear [n, k; q] code C over GF(q) is the sequence (d
1, d
2, . . . , d
k
) where d
r
is the smallest support of an r-dimensional subcode of C. An [n, k; q] code is external non-chain if for any r and s, where 1≦rs≦k, there are no subspaces D and E, such that D⊂E, dim D=r, dim E=s, w
S
(D)=d
r
, and w
S
(E)=d
s
. B...

The weight hierarchy of a linear [n,k;q] code C over GF(q) is the
sequence (d<sub>1</sub>,d<sub>2</sub>,...d<sub>k</sub>) where
d<sub>τ</sub> is the smallest support of an τ-dimensional
subcode of C. The possible weight hierarchies of [n,4;q] codes are
studied. In particular, the possible weight hierarchies of [n,4;3] codes
are determined

Improved lower bounds on multiple distinct sums sets are given. Lower bounds for the more general case of multiple difference set of a distinct sum set are considered.

A new and improved asymptotic lower bound on the maximal element of aK-sequence is given.

We give a lower bound on the maximal element in a multiple difference set.

## Citations

... The ultimate goal of researches on RGHW is to determine its exact value for any linear code and any subcode but it is really hard to achieve. Alternatively, recent researches are mainly on two topics: bounds on RGHW and related code constructions [4,[8][9][10][11][12], and the exact values of RGHW for specific classes of linear codes and subcodes [13][14][15][16]. In this study, we focus on the first topic by investigating non-asymptotic and asymptotic bounds on RGHW. ...

... Representing a system in a canonical form is very meaningful for system analysis and design. For a min-max system composed of a set of min-max functions, for instance, several analysis, control and optimization problems have been investigated based on the canonical form (see, e.g., [5,7,16,[24][25][26]). In contrast to the implicit equation given in [3,Proposition 5], which converts the matrix expression for a logical system into an irregular form of the logical expression, formula (17) presented in Algorithm 2 is an explicit equation for reconstructing the logical dynamic equations from the state transition matrix of the logical system, by which means the matrix expression is directly converted into a canonical form of the logical expression. ...

... Based on such a canonical form, some interesting results with profound significance have been obtained in max-min systems, such as the duality theorem [7] and constructive fixed point theorem [5], and some control problems are also considered (see e.g. [2,16,17]). It is known that any Boolean function can be put into a minterm canonical form [15]. Based on such a canonical form, we will give a direct conversion from the logic expression to the matrix expression of a BN in this paper. ...

... It turns out that q-systems are the vectorial counterpart of linear sets [16,24] and although we did not know about them, they appear to be well studied geometric objects, there are many works about them and recently, results about the connection between linear sets and rank metric codes were presented [3,4,19,26,29]. Going back to Hamming metric codes, in their work, [17], Liu and Chen give some properties of constant weight linear codes. Another result of Bonisoli [1] also gives a characterization of constant weight linear codes. ...

... Initially, the values for S(n, 3) were produced strictly by brute force. This process was aided by knowing that fact that the only condition that needed to be checked was i + n to j + j. ...

Reference: An Investigation of Distinct Sum Sets

... In [3] and [1] one describes and treats greedy weights of linear codes C over finite fields. First we recall the definitions of the generalized Hamming weights introduced by Wei [22]: ...

Reference: Greedy weights for matroids

... In the 1990's (and early 2000's) several authors (see e.g. [4][5][6][7][18][19][20]) became interested not only in the individual subcodes of each dimension that where optimal with respect to (small) support size, but also in chains of codes that where somehow optimal, in a similar way. This gave rise to various definitions of greedy weights, which we will recall in Sect. ...

Reference: Greedy weights for matroids

... The structure of one-weight ℤ2ℤ4-additive codes have been determined by Dougherty et al. [6]. Relative one-weight linear codes were introduced by Liu and Chen over finite fields [12] and [13]. Automorphism groups of Grassmann codes were discussed by Sudhir R. Ghorpade and Krishna V. Kaipa [14]. ...

Reference: Relative Two-Weight ℤ_2 ℤ_4 -Additive Codes

... A chain good weight hierarchy over GF (q) is also called a " chain good weight hierarchy. " There are a large number of linear block codes satisfying the chain condition; see [1, 2, 3, 5, 6, 8]. Their chain good weight hierarchies form an important group in classifying all possible weight hierarchies and they receive much attention. ...

... The concept of chain condition for codes over finite fields, especially binary and ternary fields including their relationship to trellis description, soft-decision decoding and efficient coordinate ordering has been studied very well (see [28,26,24,23,22,18,17,15,13,12] etc.) Recently, codes over rings have increased in importance, generating much interest, for example see [8,6] etc. The concept of chain condition for linear codes over GF (q) was also found useful in expressing weight hierarchies of a product code in terms of the weight hierarchies of its component codes. ...