Author

Xuan Wang

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Preprint Oct 2026

The rank of $\mathbb{Z}_{2^s}$-linear Hadamard codes

The canonical $\mathbb{Z}_{2^s}$-linear Hadamard codes are the Gray images of the $\mathbb{Z}_{2^s}$-additive codes. Their rank, the dimension of the binary linear span, was known in closed form only for $s\le 3$, and for $s \ge 4$ only through computer computations for small lengths. We give a method that computes the...

Xuan Wang, Min-Jia Shi · 0 citations

Jul 2026

Cyclic codes and cyclically covering subspaces

A subspace of $\mathbb{F}_q^n$ is called cyclically covering if the union of $\sigma^i(U)$ can cover the whole space $\mathbb{F}_q^n$, where $\sigma$ is the cyclic shift, $0 \leqslant i \leqslant n-1$. Let $h_q(n)$ be the largest possible co-dimension of a cyclically covering subspace of $\mathbb{F}_q^n$. We show that...

Xuan Wang, Minjia Shi · arXiv.org · 0 citations