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

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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 3≤k≤n−33\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.

References

Primary source

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

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