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 "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

Includes members:
  Member "pir with low storage overhead coding instead of replication":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a combinatorial view of the service rates of codes problem its equivalence to fractional matching and its connection with batch codes")
  Member "locality and availability in distributed storage":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on optimal locally repairable codes and generalized sector disk 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)