Minjia Shi

activity

20132026

most citedTwo new families of two-weight codes

86 citations · 421 across the 84 of their papers we have counts for

collaborators

87 papers

cs.IT2026

Weight spectra of some families of GRM codes

Minjia Shi, Zhaokang Xing, Patrick Sole

Let $RM_{q} (r, m)$ denote the generalized Reed--Muller code of order $r$ and length $q^{m}$ over the finite field $F_{q}$ . We completely determine the weight spectra of…

cs.CR2025

New characterization of full weight spectrum one-orbit cyclic subspace codes

Minjia Shi, Wenhao Song

Castello $et al$ . [J. Comb. Theory Ser. A, 212, 106005 (2025)] provided a complete classification for full weight spectrum (FWS) one-orbit cyclic subspace codes. In this p…

math.CO2025

The log concavity of two graphical sequences

Minjia Shi, Lu Wang, Patrick Sole

We show that the large Cartesian powers of any graph have log-concave valencies with respect to a ffxed vertex. We show that the series of valencies of distance regular graphs is l…

cs.IT2024

Triorthogonal Codes and Self-dual Codes

Minjia Shi, Haodong Lu, Jon-Lark Kim +1

Triorthogonal matrices were introduced in Quantum Information Theory in connection with distillation of magic states (Bravyi and Haah (2012)). We give an algorithm to construct bin…

cs.IT2024

Some $3$ -designs invariant under $2. P Σ L (2, 49) .$

Minjia Shi, Ruowen Liu, Patrick Solé

We construct a ternary [49,25,7] code from the row span of a Jacobsthal matrix. It is equivalent to a Generalized Quadratic Residue (GQR) code in the sense of van Lint and MacWilli…

cs.CR2023

Butson Hadamard matrices, bent sequences, and spherical codes

Minjia Shi, Danni Lu, Andrés Armario +3

We explore a notion of bent sequence attached to the data consisting of an Hadamard matrix of order $n$ defined over the complex $q^{t h}$ roots of unity, an eigenvalue of that matr…

cs.IT2023

A quaternary analogue of Tang-Ding codes

Minjia Shi, Sihui Tao, Jon-Lark Kim +1

In a recent paper, Tang and Ding introduced a class of binary cyclic codes of rate close to one half with a designed lower bound on their minimum distance. The definition involves…

math.NT2023

A new method for solving the equation $x^{d} + (x + 1)^{d} = b$ in $F_{q^{4}}$ where $d = q^{3} + q^{2} + q - 1$

Liqin Qian, Minjia Shi, Wei Lu

In this paper, we give a new method answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski about the equation $x^{d} + (x + 1)^{d} = b$ in $\mathbb{F}_…

cs.IT2023

Characterization of Plotkin-optimal two-weight codes over finite chain rings and related applications

Shitao Li, Minjia Shi

Few-weight codes over finite chain rings are associated with combinatorial objects such as strongly regular graphs (SRGs), strongly walk-regular graphs (SWRGs) and finite geometrie…

math.CO2023★ 3 cited

Quasi-cyclic perfect codes in Doob graphs and special partitions of Galois rings

Minjia Shi, Xiaoxiao Li, Denis S. Krotov +1

The Galois ring GR $(4^{Δ})$ is the residue ring $Z_{4} [x] / (h (x))$ , where $h (x)$ is a basic primitive polynomial of degree $Δ$ over $Z_{4}$ . For any odd $Δ$ larger than $1$ , we construct…

cs.IT2023★ 1 cited

Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances

Minjia Shi, Shitao Li, Tor Helleseth +1

The purpose of this paper is two-fold. First, we characterize the existence of binary self-orthogonal codes meeting the Griesmer bound by employing Solomon-Stiffler codes and some…

cs.IT2022★ 5 cited

A family of diameter perfect constant-weight codes from Steiner systems

Minjia Shi, Yuhong Xia, Denis S. Krotov

If $S$ is a transitive metric space, then $∣ C ∣ \cdot ∣ A ∣ \leq ∣ S ∣$ for any distance- $d$ code $C$ and a set $A$ , ``anticode'', of diameter less than $d$ . For every Steiner S $(t, k, n)$ s…

cs.IT2022

Optimal quaternary linear codes with one-dimensional Hermitian hull and the related EAQECCs

Shitao Li, Minjia Shi, Huizhou Liu

Linear codes with small hulls over finite fields have been extensively studied due to their practical applications in computational complexity and information protection. In this p…

cs.IT2022★ 1 cited

A tight upper bound on the number of non-zero weights of a quasi-cyclic code

Xiaoxiao Li, Minjia Shi, San Ling

Let $C$ be a quasi-cyclic code of index $l (l \geq 2)$ . Let $G$ be the subgroup of the automorphism group of $C$ generated by $ρ^{l}$ and the scalar multiplications…

cs.IT2022★ 1 cited

Characterization and construction of optimal binary linear codes with one-dimensional hull

Shitao Li, Minjia Shi, Jon-Lark Kim

The hull of a linear code over finite fields is the intersection of the code and its dual, and linear codes with small hulls have applications in computational complexity and infor…

cs.IT2022★ 3 cited

Constructing MRD codes by switching

Minjia Shi, Denis S. Krotov, Ferruh Özbudak

MRD codes are maximum codes in the rank-distance metric space on $m$ -by- $n$ matrices over the finite field of order $q$ . They are diameter perfect and have the cardinality $q^{m(n-…

cs.IT2022★ 1 cited

Cyclic codes from low differentially uniform functions

Sihem Mesnager, Minjia Shi, Hongwei Zhu

Cyclic codes have many applications in consumer electronics, communication and data storage systems due to their efficient encoding and decoding algorithms. An efficient approach t…

cs.IT2022

Two conjectures on the largest minimum distances of binary self-orthogonal codes with dimension 5

Minjia Shi, Shitao Li, Jon-Lark Kim

The purpose of this paper is to solve the two conjectures on the largest minimum distance $d_{so} (n, 5)$ of a binary self-orthogonal $[n, 5]$ code proposed by Kim and Choi (IEEE Tran…

cs.IT2022

Several classes of Galois self-orthogonal MDS codes and related applications

Yang Li, Yunfei Su, Shixin Zhu +2

Let $q = p^{h}$ be a prime power and $e$ be an integer with $0 \leq e \leq h - 1$ . $e$ -Galois self-orthogonal codes are generalizations of Euclidean self-orthogonal codes ( $e = 0$ ) and Hermi…

cs.IT2022

Rank and pairs of Rank and Dimension of Kernel of $Z_{p} Z_{p^{2}}$ -linear codes

Xiaoxiao Li, Minjia Shi, Shukai Wang

A code $C$ is called $Z_{p} Z_{p^{2}}$ -linear if it is the Gray image of a $Z_{p} Z_{p^{2}}$ -additive code. For any prime number $p$ larger than $3$ , the…

cs.IT2022

$Z_{p} Z_{p^{2}}$ -additive cyclic codes: kernel and rank

Xuan Wang, Minjia Shi

A code $C = Φ (C)$ is called $Z_{p} Z_{p^{2}}$ -linear if it's the Gray image of the $Z_{p} Z_{p^{2}}$ -additive code $C$ . In this pape…

cs.IT2022

Gray Images of Cyclic Codes over $Z_{p^{2}}$ and $\mathbb{Z}_p\mathbb{Z}_{p^2}

Minjia Shi, Xuan Wang

In the paper, we firstly study the algebraic structures of $Z_{p} Z_{p^{k}}$ -additive cyclic codes and give the generator polynomials and the minimal spanning set of…

cs.IT2022

Several constructions of optimal LCD codes over small finite fields

Shitao Li, Minjia Shi, Huizhou Liu

Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applic…

math.CO2022★ 1 cited

On the coset graph construction of distance-regular graphs

Minjia Shi, Denis S. Krotov, Patrick Solé

We show that no more new distance-regular graphs in the tables of the book of (Brouwer, Cohen, Neumaier, 1989) can be produced by using the coset graph of additive completely regul…

Weight spectra of some families of GRM codes

New characterization of full weight spectrum one-orbit cyclic subspace codes

The log concavity of two graphical sequences

Triorthogonal Codes and Self-dual Codes

Some 3-designs invariant under 2.PΣL(2,49).

Butson Hadamard matrices, bent sequences, and spherical codes

A quaternary analogue of Tang-Ding codes

A new method for solving the equation xd+(x+1)d=b in Fq4​ where d=q3+q2+q−1

Characterization of Plotkin-optimal two-weight codes over finite chain rings and related applications

Quasi-cyclic perfect codes in Doob graphs and special partitions of Galois rings

Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances

A family of diameter perfect constant-weight codes from Steiner systems

Optimal quaternary linear codes with one-dimensional Hermitian hull and the related EAQECCs

A tight upper bound on the number of non-zero weights of a quasi-cyclic code

Characterization and construction of optimal binary linear codes with one-dimensional hull

Constructing MRD codes by switching

Cyclic codes from low differentially uniform functions

Two conjectures on the largest minimum distances of binary self-orthogonal codes with dimension 5

Several classes of Galois self-orthogonal MDS codes and related applications

Rank and pairs of Rank and Dimension of Kernel of Zp​Zp2​-linear codes

Zp​Zp2​-additive cyclic codes: kernel and rank

Gray Images of Cyclic Codes over Zp2​ and $\mathbb{Z}_p\mathbb{Z}_{p^2}

Several constructions of optimal LCD codes over small finite fields

On the coset graph construction of distance-regular graphs

Some $3$ -designs invariant under $2. P Σ L (2, 49) .$

A new method for solving the equation $x^{d} + (x + 1)^{d} = b$ in $F_{q^{4}}$ where $d = q^{3} + q^{2} + q - 1$

Rank and pairs of Rank and Dimension of Kernel of $Z_{p} Z_{p^{2}}$ -linear codes

$Z_{p} Z_{p^{2}}$ -additive cyclic codes: kernel and rank

Gray Images of Cyclic Codes over $Z_{p^{2}}$ and $\mathbb{Z}_p\mathbb{Z}_{p^2}