12th ICTS Abstracts

Insertions, deletions, and substitutions are fundamental error types arising in a variety of data storage and communication systems, particularly in emerging DNA-based data storage, where such errors occur with high probabilities. The design of codes for correcting such edit errors has been extensively studied for several decades, with significant progress and strong coding results for multiple-error settings. Nevertheless, several interesting and fundamental problems remain open even in the simple setting of a single edit error. In this talk, we revisit these fundamental single-error problems and present two approaches toward simple and efficient non-binary edit-error-correcting codes.

k-uniform quantum states are important objects in quantum information theory with applications in quantum secret sharing and quantum information masking. k-uniform states in n-party q-qudit systems are also equivalent to ((n, 1, k + 1))q quantum error correction codes. In this talk, we will introduce recent progress on the upper bounds on the parameter k of k-uniform states, including shadow bounds and generalized Scott's bound.

Major blockchains such as Bitcoin and Ethereum deliberately limit transaction throughput to preserve security, processing roughly 7-15 transactions per second - far fewer than traditional payment networks such as Visa and Mastercard, which can handle thousands or even tens of thousands. This talk explores the Layer 2 scaling strategy outlined in Ethereum's roadmap and advanced by the Fusaka upgrade in December 2025. The approach aims to enable the secure processing of hundreds of thousands of transactions per second through Data Availability Sampling. At its technical core lies an elegant combination of Reed-Solomon erasure codes and the KZG polynomial commitment scheme, built using pairings on elliptic curves.