3 citations · 3 across the 17 of their papers we have counts for
8 papers · 1 filter
Algorithmic List Decoding at Capacity and Optimal Proximity Gaps for Reed-Solomon Codes
Fernando Granha Jeronimo
We give a unified hidden-derivative framework for list decoding and mutual correlated agreement of ordinary Reed--Solomon codes over prime fields, on arbitrary prescribed evaluatio…
The Honeycomb Framework for Code Bounds
William Gay, Fernando Granha Jeronimo, Lenny Liu
We introduce the honeycomb hierarchy, a representation-theoretic framework that gives new asymptotic upper bounds on . Its first level is the two-row hyperoctahedral repres…
Optimal Proximity Gap for Folded Reed--Solomon Codes via Subspace Designs
Fernando Granha Jeronimo, Lenny Liu, Pranav Rajpal
A collection of sets satisfies a -proximity gap with respect to some property if for every set in the collection, either (i) all members of the set are -close t…
Probabilistic Guarantees to Explicit Constructions: Local Properties of Linear Codes
Fernando Granha Jeronimo, Nikhil Shagrithaya
We present a general framework for derandomizing random linear codes with respect to a broad class of properties, known as local properties, which encompass several standard notion…
Explicit Codes approaching Generalized Singleton Bound using Expanders
Fernando Granha Jeronimo, Tushant Mittal, Shashank Srivastava +1
We construct a new family of explicit codes that are list decodable to capacity and achieve an optimal list size of . In contrast to existing explicit constructions o…
Higher-order Delsarte Dual LPs: Lifting, Constructions and Completeness
Leonardo Nagami Coregliano, Fernando Granha Jeronimo, Chris Jones +2
A central and longstanding open problem in coding theory is the rate-versus-distance trade-off for binary error-correcting codes. In a seminal work, Delsarte introduced a family of…