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 "rank metric codes and their duality theory"):
  Abstract: We compare the two duality theories of rank-metric codes proposed by Delsarte and Gabidulin, proving that the former generalizes the latter. We also give an elementary proof of MacWilliams identities for the general case of Delsarte rank-metric codes. The identities which we derive are very easy to handle, and allow us to re-establish in a very concise way the main results of the theory of rank-metric codes first proved by Delsarte employing the theory of association schemes and regular semilattices. We also show that our identities imply as a corollary the original MacWilliams identities established by Delsarte. We describe how the minimum and maximum rank of a rank-metric code relate to the minimum and maximum rank of the dual code, giving some bounds and characterizing the codes attaining them. Then we study optimal anticodes in the rank metric, describing them in terms of optimal codes (namely, MRD codes). In particular, we prove that the dual of an optimal anticode is an optimal anticode. Finally, as an application of our results to a classical problem in enumerative combinatorics, we derive both a recursive and an explicit formula for the number of $k \times m$ matrices over a finite field with given rank and $h$-trace.

Includes members:
  Member "fourier reflexive partitions and macwilliams identities for additive codes":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "partitions of matrix spaces with an application to q rook polynomials")
  Member "universal secure network coding via rank metric codes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "roos bound for skew cyclic codes in hamming and rank metric")
  Member "on metrics for error correction in network coding":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "point line incidence on grassmannians and majority logic decoding of grassmann codes")
  Member "a rank metric approach to error control in random network coding":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "roos bound for skew cyclic codes in hamming and rank metric")
  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")
  Member "macwilliams identity for codes with the rank metric":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "partitions of matrix spaces with an application to q rook polynomials")
  Member "macwilliams identity for the rank metric":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "rank distribution of delsarte 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)