86 citations · 421 across the 84 of their papers we have counts for
13 papers · 1 filter
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…
An enumeration of 1-perfect ternary codes
Minjia Shi, Denis S. Krotov
We study codes with parameters of the ternary Hamming code, i.e., ternary -perfect codes. The rank of the code is defined to be the dimension of its af…
On -ary shortened--perfect-like codes
Minjia Shi, Rongsheng Wu, Denis S. Krotov
We study codes with parameters of -ary shortened Hamming codes, i.e., . Firstly, we prove the fact mentioned in 1998 by Brouwer et al. that such…
The -ary antiprimitive BCH codes
Hongwei Zhu, Minjia Shi, Xiaoqiang Wang +1
It is well-known that cyclic codes have efficient encoding and decoding algorithms. In recent years, antiprimitive BCH codes have attracted a lot of attention. The objective of thi…
The connections among Hamming metric, -symbol metric, and -th generalized Hamming metric
Minjia Shi, Hongwei Zhu, Tor Helleseth
The -th generalized Hamming metric and the -symbol metric are two different generalizations of Hamming metric. The former is used on the wire-tap channel of Type II, and the…
Self-orthogonal codes over a non-unital ring and combinatorial matrices
Minjia Shi, Shukai Wang, Jon-Lark Kim +1
There is a local ring of order without identity for the multiplication, defined by generators and relations as $E=\langle a,b \mid 2a=2b=0,\, a^2=a,\, b^2=b,\,ab=a,\, ba=b…
Designs, permutations, and transitive groups
Minjia Shi, XiaoXiao Li, Patrick Solé
A notion of -designs in the symmetric group on letters was introduced by Godsil in 1988. In particular -transitive sets of permutations form a -design. We derive speci…
LCD Codes from tridiagonal Toeplitz matrice
Minjia Shi, Ferruh Özbudak, Li Xu +1
Double Toeplitz (DT) codes are codes with a generator matrix of the form with a Toeplitz matrix, that is to say constant on the diagonals parallel to the main. When …
On isodual double Toeplitz codes
Minjia Shi, Li Xu, Patrick Solé
Double Toeplitz (shortly DT) codes are introduced here as a generalization of double circulant codes. We show that such a code is isodual, hence formally self-dual. Self-dual DT co…
Designs in finite metric spaces: a probabilistic approach
Minjia Shi, Olivier Rioul, Patrick Solé
A finite metric space is called here distance degree regular if its distance degree sequence is the same for every vertex. A notion of designs in such spaces is introduced that gen…
Zero sum sets in abelian groups
Minjia Shi, Denis S. Krotov, Xiaoxiao Li +1
The distribution of cardinalities of zero-sum sets in abelian groups is completely determined. A complex summation involving the Möbius function is given for the general abelian gr…