Author

Gao-Jun Luo

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Preprint Oct 2026

On the maximum length of cyclic MDS codes

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

Preprint Sep 2026

Subspace coverings and generalized covering radii of generalized Zetterberg codes

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

Jul 2026

Entanglement-Assisted Quantum Locally Recoverable Codes: Characterizations, Bounds, and Constructions

This work introduces entanglement-assisted quantum locally recoverable codes (EAQLRCs) by assuming that halves of the pre-shared maximally entangled pairs are noiseless and establishes an upper bound on locality and a Singleton-like bound for arbitrary CSS-like EAQLRCs, and characterize the pure codes attaining equalit...

Yang Li, San Ling, Zhen-Liang Lu et al. · arXiv.org · 3 citations · ⚡1