human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "lower bound on the redundancy of pir codes"
  Abstract: We prove that the redundancy of a k-server PIR code of dimension s is Ω( √ s) for all k > 3. This coincides with a known upper bound of O( √ s) on the redundancy of PIR codes. The same lower bound was proved independently by Mary Wootters [3] using a different method. Given two binary vectors u = (u1, u2, . . . , un) and v = (v1, v2, . . . , vn), we define their product uv componentwise, namely uv def = (u1v1, u2v2, . . . , unvn) (1) where u1v1, u2v2, . . . , unvn are computed in GF(2). Note that the product operation in (1) distributes over addition in Fn 2 . Thus (1) turns the vector space F n 2 into an algebra An over F2. This algebra An is unital, associative, and commutative. Given a set X ⊆ Fn 2 , we define the square of X as the set of products of the elements in X. Explicitly, X is defined as follows: X def = { uv : u, v ∈ X } (2) The following lemmas follow straightforwardly from the definitions in (1) and (2), along with the fact that An is a commutative algebra. We let 〈X〉 denote the linear span over F2 of a set X ⊆ Fn 2 . Lemma 1. |X2| 6 |X| ( |X|+ 1 ) /2. Proof. If |X| = r, then X consists of the ( 2 ) vectors uv = vu for some u 6= v in X, along with the r vectors uu = u for some u ∈ X. Some of these vectors may coincide. Lemma 2. If a, b ∈〈X〉, then ab ∈ 〈 X 〉 . Proof. Let X = {x1, x2, . . . , xr}. Write a = ∑i αixi and b = ∑i βixi for some binary coefficients α1, α2, . . . αr, β1β2, . . . , βr. Then

Connected through hyperedge HE-1 (induced by source paper "pir codes with short block length"):
  with members:
    - "batch and pir codes and their connections to locally repairable codes"
    - "determining the generalized hamming weight hierarchy of the binary projective reed muller code"
    - "lengthening and extending binary private information retrieval codes"
    - "t private information retrieval schemes using transitive codes"
    - "locality via partially lifted codes"
    - "pir with low storage overhead coding instead of replication"
    - "achieving arbitrary locality and availability in binary codes"
    - "locality and availability in distributed storage"

Connected through hyperedge HE-2 (induced by source paper "lifted reed solomon codes with application to batch codes"):
  with members:
    - "lifted multiplicity codes and the disjoint repair group property"
    - "constructions of batch codes via finite geometry"
    - "batch and pir codes and their connections to locally repairable codes"
    - "nearly optimal constructions of pir and batch codes"
    - "high rate locally correctable codes via lifting"
    - "new affine invariant codes from lifting"

Connected through hyperedge HE-3 (induced by source paper "on the storage cost of private information retrieval"):
  with members:
    - "how to use undiscovered information inequalities direct applications of the copy lemma"
    - "breaking the mds pir capacity barrier via joint storage coding"
    - "an open source toolbox for computer aided investigation on the fundamental limits of information systems version 0 1"
    - "capacity achieving private information retrieval codes from mds coded databases with minimum message size"
    - "improved storage for efficient private information retrieval"
    - "the capacity of private information retrieval from uncoded storage constrained databases"
    - "capacity achieving private information retrieval codes with optimal message size and upload cost"
    - "on the capacity of locally decodable codes"

Connected through hyperedge HE-4 (induced by source paper "breaking the mds pir capacity barrier via joint storage coding"):
  with members:
    - "the capacity of private information retrieval from heterogeneous uncoded caching databases"
    - "an optimal iterative placement algorithm for pir from heterogeneous storage constrained databases"
    - "capacity achieving private information retrieval codes from mds coded databases with minimum message size"
    - "the capacity of private information retrieval from uncoded storage constrained databases"
    - "batch and pir codes and their connections to locally repairable codes"
    - "on the fundamental limit of private information retrieval for coded distributed storage"
    - "private information retrieval from mds coded data in distributed storage systems"
    - "on sub packetization and access number of capacity achieving pir schemes for mds coded non colluding servers"

Connected through hyperedge HE-5 (induced by source paper "lifted multiplicity codes and the disjoint repair group property"):
  with members:
    - "batch and pir codes and their connections to locally repairable codes"
    - "nearly optimal constructions of pir and batch codes"
    - "locality via partially lifted codes"
    - "bounds on the parameters of locally recoverable codes"
    - "high rate locally correctable and locally testable codes with sub polynomial query complexity"
    - "repair locality with multiple erasure tolerance"
    - "locality and availability in distributed storage"
    - "bounds on locally recoverable codes with multiple recovering sets"

Connected through hyperedge HE-6 (induced by source paper "constructions of batch codes via finite geometry"):
  with members:
    - "bounds on the length of functional pir and batch codes"
    - "nearly optimal constructions of pir and batch codes"
    - "on private information retrieval array codes"
    - "pir array codes with optimal pir rate"
    - "pir with low storage overhead coding instead of replication"
    - "achieving arbitrary locality and availability in binary codes"
    - "locality and availability in distributed storage"
    - "optimal combinatorial batch codes based on block designs"

Connected through hyperedge HE-7 (induced by source paper "lifted multiplicity codes"):
  with members:
    - "batch and pir codes and their connections to locally repairable codes"
    - "bounds on the parameters of locally recoverable codes"
    - "some remarks on multiplicity codes"
    - "high rate locally correctable and locally testable codes with sub polynomial query complexity"
    - "bounds on locally recoverable codes with multiple recovering sets"

Connected through hyperedge HE-8 (induced by source paper "batch and pir codes and their connections to locally repairable codes"):
  with members:
    - "on private information retrieval array codes"
    - "pir array codes with optimal pir rate"
    - "cooperative local repair in distributed storage"
    - "pir with low storage overhead coding instead of replication"
    - "private information retrieval for coded storage"
    - "bounds for batch codes with restricted query size"
    - "applications of polymatroid theory to distributed storage systems"
    - "repair locality with multiple erasure tolerance"

Question: Please tell me which class the center node 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)