We study the maximum length of nontrivial simple-root cyclic maximum distance separable (MDS) codes over ${\mathbb F}_q$. We prove $n\le q+1$ if $\gcd(n,q^2-1)>2$, or if the dimension is even and $\gcd(n,q^2-1)>1$. The bound also holds for all lengths whose prime factors lie in $\{2,3,5,7\}$. We obtain further cases in...
Gao-Jun Luo, Xi-Wang Cao, Shi-Tao Li et al.· 0 citations
This paper investigates the quantum chromatic number of generalized Johnson graphs and determines the exact quantum chromatic numbers of two infinite families of generalized Johnson graphs, which exhibit an exponential separation between the classical and quantum chromatic numbers.
Gao-Jun Luo, Xi-Wang Cao, Shi-Tao Li et al.· 0 citations
Generalized covering radii measure how many columns of a parity-check matrix are needed to generate several syndromes simultaneously. Their finite-geometric counterparts are $(\rho,t)$-saturating sets, for which every $t$-dimensional subspace is contained in a subspace generated by at most $\rho$ prescribed vectors. We...
Shi-Tao Li, Yang Li, Gao-Jun Luo et al.· 1 citation
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