86 citations · 421 across the 84 of their papers we have counts for
16 papers · 1 filter
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…
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 is the residue ring , where is a basic primitive polynomial of degree over . For any odd larger than , we construct…
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…
Self-dual Hadamard bent sequences
Minjia Shi, Yaya Li, Wei Cheng +3
A new notion of bent sequence related to Hadamard matrices was introduced recently, motivated by a security application ( Solé et al, 2021). We study the self dual class in length…
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…
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…
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…
On the number of frequency hypercubes
Minjia Shi, Shukai Wang, Xiaoxiao Li +1
A frequency -cube is an -dimensional -by-...-by- array filled by s and s such that each line contains exactly two s. We classify the frequency …
Three-weight codes over rings and strongly walk regular graphs
Michael Kiermaier, Sascha Kurz, Minjia Shi +1
We construct strongly walk-regular graphs as coset graphs of the duals of codes with three non-zero homogeneous weights over for a prime, and more generally…
On the number of resolvable Steiner triple systems of small 3-rank
Minjia Shi, Li Xu, Denis S. Krotov
In a recent work, Jungnickel, Magliveras, Tonchev, and Wassermann derived an overexponential lower bound on the number of nonisomorphic resolvable Steiner triple systems (STS) of o…
Sufficient conditions for STS of 3-rank to be resolvable
Yaqi Lu, Minjia Shi
Based on the structure of non-full--rank and the orthogonal Latin squares, we mainly give sufficient conditions for of -rank to be resolvab…
The Steiner triple systems of order 21 with a transversal subdesign TD(3,6)
Yue Guan, Minjia Shi, Denis S. Krotov
We prove several structural properties of Steiner triple systems (STS) of order 3w+3 that include one or more transversal subdesigns TD(3,w). Using an exhaustive search, we find th…
A new distance-regular graph of diameter 3 on 1024 vertices
Minjia Shi, Denis Krotov, Patrick Solé
The dodecacode is a nonlinear additive quaternary code of length . By puncturing it at any of the twelve coordinates, we obtain a uniformly packed code of distance . In part…
The number of the non-full-rank Steiner triple systems
Minjia Shi, Li Xu, Denis S. Krotov
The -rank of a Steiner triple system is the dimension of the linear span of the set of characteristic vectors of blocks of , over GF. We derive a formula for the num…