A Tight Upper Bound for the Maximal Length of MDS Elliptic Codes

Determining the maximal length of MDS codes with certain dimension is one of the central topics in coding theory and finite geometry. The MDS Main Conjecture states that the maximal length of a non-trivial $q$-ary MDS code of dimension $k$ is $q+1$ except when $q$ is even and $k=3$ or $k=q-1$. We prove that the maximal length of non-trivial $q$-ary MDS elliptic codes is close to $\frac{q}{2}$, which gives an affirmative answer to a conjecture of Li, Wan, and Zhang. Moreover, we apply our result to derive an answer to a question on subset sums in finite abelian groups from elliptic curves.

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On Deep Holes of Elliptic Curve Codes

Zhang

Wan

2023

IEEE Trans. Inform. Theory

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A Tight Upper Bound for the Maximal Length of MDS Elliptic Codes

Cited by 5 publications

References 28 publications

Near MDS codes of non-elliptic-curve type from Reed-Solomon codes

Near MDS codes of non-elliptic-curve type from Reed-Solomon codes

The Maximal Length of q-ary MDS Elliptic Codes Is Close to

On Deep Holes of Elliptic Curve Codes

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