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 "macwilliams extension theorems and the local global property for codes over rings"):
  Abstract: The MacWilliams extension theorem is investigated for various weight functions over finite Frobenius rings. The problem is reformulated in terms of a local-global property for subgroups of the general linear group. Among other things, it is shown that the extension theorem holds true for poset weights if and only if the underlying poset is hierarchical. Specifically, the Rosenbloom-Tsfasman weight for vector codes satisfies the extension theorem, whereas the Niederreiter-Rosenbloom-Tsfasman weight for matrix codes does not. A short character-theoretic proof of the well-known MacWilliams extension theorem for the homogeneous weight is provided. Moreover it is shown that the extension theorem carries over to direct products of weights, but not to symmetrized products.

Includes members:
  Member "linear codes on posets with extension property":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "characterization of metrics induced by hierarchical posets")
  Member "the homogeneous weight partition and its character theoretic dual":
    also connected through other hyperedges:
      (none)
  Member "fourier reflexive partitions and macwilliams identities for additive codes":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "partitions of matrix spaces with an application to q rook polynomials")
  Member "equivalence for rank metric and matrix codes and automorphism groups of gabidulin codes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "equivalence and characterizations of linear rank metric codes based on invariants")
  Member "partitions of frobenius rings induced by the homogeneous weight":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "partitions of matrix spaces with an application to q rook polynomials")

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)