Advances in Elliptic Curve Codes and Streaming Codes

The field of coding theory is witnessing significant developments, particularly in the construction of optimal codes and the analysis of streaming codes. Researchers are exploring new approaches to construct optimal codes, such as using algebraic function fields and elliptic curves, to achieve better performance in distributed storage systems. Meanwhile, the analysis of streaming codes is gaining attention, with a focus on understanding their fundamental limits and improving their error probability in stochastic channels. Notably, the use of elliptic curves is becoming increasingly prominent, with applications in cryptography and code construction. Some papers are pushing the boundaries of code construction, introducing new families of codes and investigating their properties. Overall, the field is moving towards more efficient and secure coding schemes, with a growing interest in elliptic curve-based constructions. Noteworthy papers include: New Constructions of Optimal (r,δ)-LRCs via Algebraic Function Fields, which presents new constructions of optimal codes using algebraic function fields. On the Analysis of Random Linear Streaming Codes in Stochastic Channels, which derives closed-form expressions for the error probability of streaming codes in stochastic channels. ECCFROG522PP: An Enhanced 522-bit Weierstrass Elliptic Curve, which introduces a new elliptic curve with improved security and verifiability.

Sources

New Constructions of Optimal $(r,\delta)$-LRCs via Algebraic Function Fields

On the Analysis of Random Linear Streaming Codes in Stochastic Channels

On a class of twisted elliptic curve codes

ECCFROG522PP: An Enhanced 522-bit Weierstrass Elliptic Curve

Non-Reed-Solomon Type MDS Codes from Elliptic Curves

Cryptographic Application of Elliptic Curve with High Rank

Marginal sets in semigroups and semirings

On catastrophicity of convolutional codes and their encoders over $\Z_{p^r}$

Rate-Optimal Streaming Codes over Three-Node Relay Networks with Burst Erasures

Row-Column Twisted Reed-Solomon codes

Deep holes of a class of twisted Reed-Solomon codes

Built with on top of