7 papers
Proximity Gaps for Gabidulin Codes and Applications
Songsong Li, Chaoping Xing, Chen Yuan +1
Proximity gaps are central to the soundness of interactive oracle proofs of proximity (IOPPs) and polynomial commitment schemes (PCSs). An linear code $C\subseteq\mathbb…
Quasi-linear time decoding of RS and AG codes for burst errors up to the Singleton bound
Songsong Li, Shu Liu, Liming Ma +2
Despite of tremendous research on decoding Reed-Solomon (RS) and algebraic geometry (AG) codes under the random and adversary substitution error models, few studies have explored t…
Coded Distributed (Batch) Matrix Multiplication over Galois Ring via RMFE
Yi Kuang, Jiang Li, Songsong Li +1
Coded Distributed Matrix Multiplication (CDMM) is a distributed matrix multiplication (DMM) for large-scale matrices through a coding scheme such that any worker node among all…
Algebraic Geometry Codes for Distributed Matrix Multiplication Using Local Expansions
Jiang Li, Songsong Li, Chaoping Xing
Code-based Distributed Matrix Multiplication (DMM) has been extensively studied in distributed computing for efficiently performing large-scale matrix multiplication using coding t…
Encoding of algebraic geometry codes with quasi-linear complexity
Songsong Li, Shu Liu, Liming Ma +2
Fast encoding and decoding of codes have been always an important topic in code theory as well as complexity theory. Although encoding is easier than decoding in general, designing…
Asymptotic construction of locally repairable codes with multiple recovering sets
Singsong Li, Shu Liu, Liming Ma +1
Locally repairable codes have been extensively investigated due to practical applications in distributed and cloud storage systems in recent years. However, not much work on asympt…
Fast Fourier transform via automorphism groups of rational function fields
Songsong Li, Chaoping Xing
The Fast Fourier Transform (FFT) over a finite field computes evaluations of a given polynomial of degree less than at a specifically chosen set of distinct…