Remarks on Johnson-type Bounds for Insdel Codes

2026-05-24

AI Summary

This work addresses the refinement of Johnson-type list decoding bounds for insertion-deletion (insdel) codes to more precisely characterize the upper bound on list size. To this end, it introduces binary constant-weight codes into the list decoding analysis of insdel codes for the first time. By encoding local lists as binary constant-weight codes, the approach improves upon the bound established by Hayashi and Yasunaga. Integrating combinatorial coding theory, constructions of constant-weight codes, and list decoding techniques, the method yields a tighter Johnson-type upper bound than existing results, thereby significantly advancing the theoretical understanding of the list decoding capability of insdel codes.

Abstract

We refine the Johnson-type list-size bound of Hayashi and Yasunaga for insertion-deletion codes by encoding local lists into binary constant-weight codes.

Problem

• insertion-deletion codes
• Johnson bound
• list decoding
• constant-weight codes

Innovation

• insertion-deletion codes
• Johnson bound
• list decoding
• constant-weight codes
• coding theory