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 "duality of codes supported on regular lattices with an application to enumerative combinatorics"):
  Abstract: We introduce a general class of regular weight functions on finite abelian groups, and study the combinatorics, the duality theory, and the metric properties of codes endowed with such functions. The weights are obtained by composing a suitable support map with the rank function of a graded lattice satisfying certain regularity properties. A regular weight on a group canonically induces a regular weight on the character group, and invertible MacWilliams identities always hold for such a pair of weights. Moreover, the Krawtchouk coefficients of the corresponding MacWilliams transformation have a precise combinatorial significance, and can be expressed in terms of the invariants of the underlying lattice. In particular, they are easy to compute in many examples. Several weight functions traditionally studied in Coding Theory belong to the class of weights introduced in this paper. Our lattice-theory approach also offers a control on metric structures that a regular weight induces on the underlying group. In particular, it allows to show that every finite abelian group admits weight functions that, simultaneously, give rise to MacWilliams identities, and endow the underlying group with a metric space structure. We propose a general notion of extremality for (not necessarily additive) codes in groups endowed with semi-regular supports, and establish a Singleton-type bound. We then investigate the combinatorics and duality theory of extremal codes, extending classical results on the weight and distance distribution of error-correcting codes. Finally, we apply the theory of MacWilliams identities to enumerative combinatorics problems, obtaining closed formulae for the number of rectangular matrices over a finite having prescribed rank and satisfying some linear conditions.

Includes members:
  Member "rank metric codes and their duality theory":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "degenerate flag varieties in network coding")
  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 "partitions of frobenius rings induced by the homogeneous weight":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "partitions of matrix spaces with an application to q rook polynomials")
  Member "on metrics for error correction in network coding":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "point line incidence on grassmannians and majority logic decoding of grassmann 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)