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 "partition balanced families of codes and asymptotic enumeration in coding theory"):
  Abstract: We introduce the class of partition-balanced families of codes, and show how to exploit their combinatorial invariants to obtain upper and lower bounds on the number of codes that have a prescribed property. In particular, we derive precise asymptotic estimates on the density functions of several classes of codes that are extremal with respect to minimum distance, covering radius, and maximality. The techniques developed in this paper apply to various distance functions, including the Hamming and the rank metric distances. Applications of our results show that, unlike the $\mathbb{F}_{q^m}$-linear MRD codes, the $\mathbb{F}_q$-linear MRD codes are not dense in the family of codes of the same dimension. More precisely, we show that the density of $\mathbb{F}_q$-linear MRD codes in $\mathbb{F}_q^{n \times m}$ in the set of all matrix codes of the same dimension is asymptotically at most $1/2$, both as $q \to +\infty$ and as $m \to +\infty$. We also prove that MDS and $\mathbb{F}_{q^m}$-linear MRD codes are dense in the family of maximal codes. Although there does not exist a direct analogue of the redundancy bound for the covering radius of $\mathbb{F}_q$-linear rank metric codes, we show that a similar bound is satisfied by a uniformly random matrix code with high probability. In particular, we prove that codes meeting this bound are dense. Finally, we compute the average weight distribution of linear codes in the rank metric, and other parameters that generalize the total weight of a linear code.

Includes members:
  Member "maximal ferrers diagram codes constructions and genericity considerations":
    also connected through other hyperedges:
      - Hyperedge HE-1 (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-2 (induced by source paper "rank metric codes")
  Member "on the genericity of maximum rank distance and 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 "repairing the faure loidreau public key cryptosystem":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "decoding high order interleaved rank metric codes")
  Member "automorphism groups of gabidulin like codes":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "mathbb f _ q n linear rank distance codes and their distinguishers")
  Member "polynomial time key recovery attack on the faure loidreau scheme based on gabidulin codes":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "decoding high order interleaved rank metric codes")
  Member "algebraic structures of mrd codes":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "partitions of matrix spaces with an application to q rook polynomials")
  Member "rank distribution of delsarte codes":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "new constructions of subspace codes using subsets of mrd codes in several blocks")

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)