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 "perfect codes in the discrete simplex"):
  Abstract: We study the problem of existence of (nontrivial) perfect codes in the discrete $$ n $$ n -simplex $$ \Delta _{\ell }^n := \left\{ \left( \begin{array}{l} x_0, \ldots , x_n \end{array}\right) : x_i \in {\mathbb {Z}}_{+}, \sum _i x_i = \ell \right\} $$ Δ l n : = x 0 , ? , x n : x i ? Z + , ? i x i = l under $$ \ell _1 $$ l 1 metric. The problem is motivated by the so-called multiset codes, which have recently been introduced by the authors as appropriate constructs for error correction in the permutation channels. It is shown that $$ e $$ e -perfect codes in the 1-simplex $$ \Delta _{\ell }^1 $$ Δ l 1 exist for any $$ \ell \ge 2e + 1 $$ l ? 2 e + 1 , the 2-simplex $$ \Delta _{\ell }^2$$ Δ l 2 admits an $$ e $$ e -perfect code if and only if $$ \ell = 3e + 1 $$ l = 3 e + 1 , while there are no perfect codes in higher-dimensional simplices. In other words, perfect multiset codes exist only over binary and ternary alphabets.

Includes members:
  Member "multiset codes for permutation channels":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "codes in the space of multisets coding for permutation channels with impairments")
  Member "subset codes for packet networks":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "codes in the space of multisets coding for permutation channels with impairments")
  Member "product constructions for perfect lee codes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "50 years of the golomb welch conjecture")
  Member "a matroid framework for noncoherent random network communications":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "probability of partially solving random linear systems in network coding")
  Member "coding for errors and erasures in random network coding":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on the gap between scalar and vector solutions of generalized combination networks")

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)