Han and Ren's maximal-length conjecture for MDS elliptic codes

Let E\mathcal{E} be an elliptic curve over Fq\mathbb{F}_q, and let CL(D,G)C_L(D,G) be an [n,k][n,k] MDS code from E\mathcal{E}. Assume that 3kn33\leq k\leq n-3. Han and Ren's conjecture. If qq is sufficiently large, then

n#E(Fq)2.n\leq \frac{\#\mathcal{E}(\mathbb{F}_q)}{2}.

This conjecture gives a maximal-length upper bound in terms of the number of rational points on the elliptic curve. The supplied text does not indicate whether it has been resolved.

Sources & referencesView supporting material

Primary source

Yunlong Zhu and Chang-An Zhao, “On Iso-Dual MDS Codes From Elliptic Curves”, arXiv:2502.02033 (2025).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.