human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "combinatorial limitations of average radius list decoding"):
  Abstract: We study certain combinatorial aspects of list-decoding, motivated by the exponential gap between the known upper bound (of $O(1/\gamma)$) and lower bound (of $\Omega_p(\log (1/\gamma))$) for the list-size needed to decode up to radius $p$ with rate $\gamma$ away from capacity, i.e., $1-\h(p)-\gamma$ (here $p\in (0,1/2)$ and $\gamma > 0$). Our main result is the following: #R##N#We prove that in any binary code $C \subseteq \{0,1\}^n$ of rate $1-\h(p)-\gamma$, there must exist a set $\mathcal{L} \subset C$ of $\Omega_p(1/\sqrt{\gamma})$ codewords such that the average distance of the points in $\mathcal{L}$ from their centroid is at most $pn$. In other words, there must exist $\Omega_p(1/\sqrt{\gamma})$ codewords with low "average radius." The standard notion of list-decoding corresponds to working with the maximum distance of a collection of codewords from a center instead of average distance. The average-radius form is in itself quite natural and is implied by the classical Johnson bound. #R##N#The remaining results concern the standard notion of list-decoding, and help clarify the combinatorial landscape of list-decoding: #R##N#1. We give a short simple proof, over all fixed alphabets, of the above-mentioned $\Omega_p(\log (\gamma))$ lower bound. Earlier, this bound followed from a complicated, more general result of Blinovsky. #R##N#2. We show that one {\em cannot} improve the $\Omega_p(\log (1/\gamma))$ lower bound via techniques based on identifying the zero-rate regime for list decoding of constant-weight codes. #R##N#3. We show a "reverse connection" showing that constant-weight codes for list decoding imply general codes for list decoding with higher rate. #R##N#4. We give simple second moment based proofs of tight (up to constant factors) lower bounds on the list-size needed for list decoding random codes and random linear codes from errors as well as erasures.

Includes members:
  Member "restricted isometry of fourier matrices and list decodability of random linear codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "one shot neural architecture search via compressive sensing")
  Member "linear algebraic list decoding of folded reed solomon codes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "beyond the guruswami sudan and parvaresh vardy radii folded reed solomon multiplicity and derivative codes")
  Member "on the list decodability of random linear codes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "ldpc codes achieve list decoding capacity")
  Member "explicit codes achieving list decoding capacity error correction with optimal redundancy":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "beyond the guruswami sudan and parvaresh vardy radii folded reed solomon multiplicity and derivative codes")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.IT(Information Theory)