112 citations · 288 across the 38 of their papers we have counts for
38 papers
From Lecture Notes to Lean: Formalizing a Textbook on Probability Theory
Shuo Deng, Kenneth W. Shum
As large language models become increasingly capable of generating mathematical arguments, mathematics is likely to face not a scarcity of proofs but an abundance of plausible ones…
Formalizing Extended Complex Numbers, Mobius Transformations, and Cross Ratio in Lean 4
Fubin Yan, Kenneth W. Shum
The extended complex plane is a fundamental object in complex analysis, hyperbolic geometry, and mathematical physics. Its geometry is governed by Möbius transformations, with the…
Regenerating codes with minimal disk I/O cost achieving optimal tradeoff between storage and repair bandwidth
Minhan Gao, Kenneth Shum
Regenerating codes achieve the fundamental tradeoff between storage efficiency and repair bandwidth in distributed storage systems. Beyond these two parameters, disk I/O cost is an…
Weight Distribution of Repeated-Root Cyclic Codes with Prime Power Lengths
Wei Zhao, Weixian Li, Shenghao Yang +2
Determining the weight distribution of a linear code is a classical and fundamental topic in coding theory that has been extensively investigated. Repeated-root cyclic codes, which…
Optimal Quaternary (r,delta)-Locally Repairable Codes Achieving the Singleton-type Bound
Kenneth W. Shum, Jie Hao
Locally repairable codes enables fast repair of node failure in a distributed storage system. The code symbols in a codeword are stored in different storage nodes, such that a disk…
Repeated-root Constacyclic Codes with Optimal Locality
Wei Zhao, Kenneth W. Shum, Shenghao Yang
A code is called a locally repairable code (LRC) if any code symbol is a function of a small fraction of other code symbols. When a locally repairable code is employed in a distrib…