86 citations · 421 across the 84 of their papers we have counts for
64 papers · 1 filter
Weight spectra of some families of GRM codes
Minjia Shi, Zhaokang Xing, Patrick Sole
Let denote the generalized Reed--Muller code of order and length over the finite field . We completely determine the weight spectra of…
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…
Some -designs invariant under
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…
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…
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…
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…
A family of diameter perfect constant-weight codes from Steiner systems
Minjia Shi, Yuhong Xia, Denis S. Krotov
If is a transitive metric space, then for any distance- code and a set , ``anticode'', of diameter less than . For every Steiner S s…
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…
A tight upper bound on the number of non-zero weights of a quasi-cyclic code
Xiaoxiao Li, Minjia Shi, San Ling
Let be a quasi-cyclic code of index . Let be the subgroup of the automorphism group of generated by and the scalar multiplications…
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…
Constructing MRD codes by switching
Minjia Shi, Denis S. Krotov, Ferruh Özbudak
MRD codes are maximum codes in the rank-distance metric space on -by- matrices over the finite field of order . They are diameter perfect and have the cardinality $q^{m(n-…
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…
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 of a binary self-orthogonal code proposed by Kim and Choi (IEEE Tran…
Several classes of Galois self-orthogonal MDS codes and related applications
Yang Li, Yunfei Su, Shixin Zhu +2
Let be a prime power and be an integer with . -Galois self-orthogonal codes are generalizations of Euclidean self-orthogonal codes () and Hermi…
Rank and pairs of Rank and Dimension of Kernel of -linear codes
Xiaoxiao Li, Minjia Shi, Shukai Wang
A code is called -linear if it is the Gray image of a -additive code. For any prime number larger than , the…
-additive cyclic codes: kernel and rank
Xuan Wang, Minjia Shi
A code is called -linear if it's the Gray image of the -additive code . In this pape…
Gray Images of Cyclic Codes over and $\mathbb{Z}_p\mathbb{Z}_{p^2}
Minjia Shi, Xuan Wang
In the paper, we firstly study the algebraic structures of -additive cyclic codes and give the generator polynomials and the minimal spanning set of…
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…
-linear codes: rank and kernel
Minjia Shi, Shukai Wang, Xiaoxiao Li
A code is called -linear if it is the Gray image of a -additive code, where is prime. In this paper, the rank and the dimension of the kernel…
Equivalence and Duality of Polycyclic Codes Associated with Trinomials over Finite Fields
Minjia Shi, Haodong Lu, Shuang Zhou +2
In this paper, several conjectures proposed in [2] are studied, involving the equivalence and duality of polycyclic codes associated with trinomials. According to the results, we g…
The b-symbol weight distribution of irreducible cyclic codes and related consequences
Hongwei Zhu, Minjia Shi
The -symbol read channel is motivated by the limitations of the reading process in high density data storage systems. The corresponding new metric is a generalization of the Ham…
The b-symbol weight hierarchy of the Kasami codes
Hongwei Zhu, Minjia Shi
The symbol-pair read channel was first proposed by Cassuto and Blaum. Later, Yaakobi et al. generalized it to the -symbol read channel. It is motivated by the limitations of the…
On the structure of -generator quasi-polycyclic codes over finite chain rings
Rongsheng Wu, Minjia Shi, Patrick Solé
Quasi-polycyclic (QP for short) codes over a finite chain ring are a generalization of quasi-cyclic codes, and these codes can be viewed as an -submodule of $\mathcal{R}_…
Complete b-symbol weight distribution of some irreducible cyclic codes
Hongwei Zhu, Minjia Shi, Ferruh Ozbudak
Recently, -symbol codes are proposed to protect against -symbol errors in -symbol read channels. It is an interesting subject of study to consider the complete -symbol…