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 "partitions of matrix spaces with an application to q rook polynomials"):
  Abstract: We study the row-space partition and the pivot partition on the matrix space $\mathbb{F}_q^{n \times m}$. We show that both these partitions are reflexive and that the row-space partition is self-dual. Moreover, using various combinatorial methods, we explicitly compute the Krawtchouk coefficients associated with these partitions. This establishes MacWilliams-type identities for the row-space and pivot enumerators of linear rank-metric codes. We then generalize the Singleton-like bound for rank-metric codes, and introduce two new concepts of code extremality. The latter are both preserved by trace-duality, and generalize the notion of an MRD code. Moreover, codes that are extremal according to either notion satisfy strong rigidity properties, analogous to those of MRD codes. As an application of our results to algebraic combinatorics, we give closed formulas for the $q$-rook polynomials associated with Ferrers diagram boards. Moreover, we exploit connections between matrices over finite fields and rook placements to prove that the number of rank $r$ matrices over $\mathbb{F}_q$ supported on a Ferrers diagram is a polynomial in $q$ whose degree is strictly increasing in $r$. We close the paper by investigating the natural analogues of the MacWilliams Extension Theorem for the rank, the row-space and the pivot partitions.

Includes members:
  Member "a polymatroid approach to generalized weights of rank metric codes":
    also connected through other hyperedges:
      (none)
  Member "rank metric codes and q polymatroids":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "rank metric codes")
  Member "maximal ferrers diagram codes constructions and genericity considerations":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on some automorphisms of rational functions and their applications in rank metric codes")
  Member "codes endowed with the rank metric":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "rank metric codes")
  Member "adversarial network coding":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "delay aware wireless network coding in adversarial traffic")
  Member "relative generalized matrix weights of matrix codes for universal security on wire tap networks":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "reliable and secure multishot network coding using linearized reed solomon codes")
  Member "algebraic structures of mrd codes":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "maximal ferrers diagram codes constructions and genericity considerations")
  Member "duality of codes supported on regular lattices with an application to enumerative combinatorics":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "rank metric codes generalized binomial moments and their zeta functions")

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)