On Deep Holes of Elliptic Curve Codes
Jun Zhang, Daqing Wan
TL;DR
This paper introduces a method to construct deep holes in elliptic curve codes and conjectures its completeness for long codes, supported by connections to finite geometry.
Contribution
It presents a novel construction method for deep holes in elliptic curve codes and conjectures its completeness, linking coding theory with finite geometry.
Findings
Proposes a new method for constructing deep holes.
Conjectures the method's completeness for long codes.
Provides evidence and heuristics based on finite geometry.
Abstract
We give a method to construct deep holes for elliptic curve codes. For long elliptic curve codes, we conjecture that our construction is complete in the sense that it gives all deep holes. Some evidence and heuristics on the completeness are provided via the connection with problems and results in finite geometry.
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Taxonomy
TopicsCryptography and Residue Arithmetic · Coding theory and cryptography