Xiaoxiao Li

activity

20182024

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

3 citations · 7 across the 9 of their papers we have counts for

collaborators

9 papers

math.CO2024

Triangle decompositions of PG(n-1,2)

Minjia Shi, Xiaoxiao Li, Denis S. Krotov

We define a triangle design as a partition of the set of lines of a projective space into triangles, where a triangle consists of three pairwise intersecting lines with no common p…

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.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

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

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

Minjia Shi, Shukai Wang, Xiaoxiao Li

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, where $p > 2$ is prime. In this paper, the rank and the dimension of the kernel…

math.CO2021★ 1 cited

Designs, permutations, and transitive groups

Minjia Shi, XiaoXiao Li, Patrick Solé

A notion of $t$ -designs in the symmetric group on $n$ letters was introduced by Godsil in 1988. In particular $t$ -transitive sets of permutations form a $t$ -design. We derive speci…

math.CO2021

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…

math.CO2020★ 2 cited

On the number of frequency hypercubes $F^{n} (4; 2, 2)$

Minjia Shi, Shukai Wang, Xiaoxiao Li +1

A frequency $n$ -cube $F^{n} (4; 2, 2)$ is an $n$ -dimensional $4$ -by-...-by- $4$ array filled by $0$ s and $1$ s such that each line contains exactly two $1$ s. We classify the frequency $4$ …

cs.IT2018

How many weights can a cyclic code have ?

Minjia Shi, Xiaoxiao Li, Alessandro Neri +1

Upper and lower bounds on the largest number of weights in a cyclic code of given length, dimension and alphabet are given. An application to irreducible cyclic codes is considered…