TL;DR
This paper extends interpolation-based decoding methods to differential algebraic geometry codes, analyzes their performance, and reveals a close relationship with evaluation AG codes, including a specific algorithm for Goppa codes.
Contribution
It demonstrates the applicability of interpolation-based decoding to differential AG codes and explores their performance and relation to evaluation codes, including Goppa codes.
Findings
Decoding capacities of evaluation and differential AG codes are closely related.
Interpolation-based decoding is effective for differential AG codes.
A new decoding algorithm for classical Goppa codes is introduced.
Abstract
The interpolation-based decoding that was developed for general evaluation AG codes is shown to be equally applicable to general differential AG codes. A performance analysis of the decoding algorithm, which is parallel to that of its companion algorithm, is reported. In particular, the decoding capacities of evaluation AG codes and differential AG codes are seen to be nicely interrelated. As an interesting special case, a decoding algorithm for classical Goppa codes is presented.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.