human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "optimal locally repairable linear codes"
  Abstract: Linear erasure codes with local repairability are desirable for distributed data storage systems. An [n, k, d] code having all-symbol (r, \delta})-locality, denoted as (r, {\delta})a, is considered optimal if it also meets the minimum Hamming distance bound. The existing results on the existence and the construction of optimal (r, {\delta})a codes are limited to only the special case of {\delta} = 2, and to only two small regions within this special case, namely, m = 0 or m >= (v+{\delta}-1) > ({\delta}-1), where m = n mod (r+{\delta}-1) and v = k mod r. This paper investigates the existence conditions and presents deterministic constructive algorithms for optimal (r, {\delta})a codes with general r and {\delta}. First, a structure theorem is derived for general optimal (r, {\delta})a codes which helps illuminate some of their structure properties. Next, the entire problem space with arbitrary n, k, r and {\delta} is divided into eight different cases (regions) with regard to the specific relations of these parameters. For two cases, it is rigorously proved that no optimal (r, {\delta})a could exist. For four other cases the optimal (r, {\delta})a codes are shown to exist, deterministic constructions are proposed and the lower bound on the required field size for these algorithms to work is provided. Our new constructive algorithms not only cover more cases, but for the same cases where previous algorithms exist, the new constructions require a considerably smaller field, which translates to potentially lower computational complexity. Our findings substantially enriches the knowledge on (r, {\delta})a codes, leaving only two cases in which the existence of optimal codes are yet to be determined.

Connected through hyperedge HE-1 (induced by source paper "on optimal locally repairable codes and generalized sector disk codes"):
  with members:
    - "array codes with local properties"
    - "universal and dynamic locally repairable codes with maximal recoverability via sum rank codes"
    - "how long can optimal locally repairable codes be"
    - "explicit construction of optimal locally recoverable codes of distance 5 and 6 via binary constant weight codes"
    - "on optimal locally repairable codes with super linear length"
    - "explicit optimal length locally repairable codes of distance 5"
    - "locality and availability of array codes constructed from subspaces"
    - "optimal locally repairable codes via elliptic curves"

Connected through hyperedge HE-2 (induced by source paper "new bounds on the field size for maximally recoverable codes instantiating grid like topologies"):
  with members:
    - "on maximally recoverable codes for product topologies"
    - "maximally recoverable lrcs a field size lower bound and constructions for few heavy parities"
    - "maximally recoverable codes for grid like topologies"
    - "binary codes with locality for multiple erasures having short block length"
    - "optimal binary locally repairable codes via anticodes"
    - "binary linear locally repairable codes"
    - "locally recoverable codes on algebraic curves"
    - "repair locality with multiple erasure tolerance"

Connected through hyperedge HE-3 (induced by source paper "erasure codes for distributed storage tight bounds and matching constructions"):
  with members:
    - "explicit msr codes with optimal access optimal sub packetization and small field size for d k 1 k 2 k 3"
    - "a tight rate bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures"
    - "optimal lrc codes for all lenghts n q"
    - "optimal locally repairable codes of distance 3 and 4 via cyclic codes"
    - "on optimal ternary locally repairable codes"
    - "liquid cloud storage"
    - "rate optimal binary linear locally repairable codes with small availability"
    - "bounds and constructions of codes with all symbol locality and availability"

Connected through hyperedge HE-4 (induced by source paper "extended integrated interleaved codes over any field with applications to locally recoverable codes"):
  with members:
    - "combinatorial alphabet dependent bounds for locally recoverable codes"
    - "optimal lrc codes for all lenghts n q"
    - "optimal locally repairable codes of distance 3 and 4 via cyclic codes"
    - "erasure coding for distributed storage an overview"
    - "maximally recoverable lrcs a field size lower bound and constructions for few heavy parities"
    - "bounds and constructions for linear locally repairable codes over binary fields"
    - "optimal binary linear locally repairable codes with disjoint repair groups"
    - "extended product and integrated interleaved codes"

Connected through hyperedge HE-5 (induced by source paper "universal and dynamic locally repairable codes with maximal recoverability via sum rank codes"):
  with members:
    - "maximally recoverable codes with hierarchical locality"
    - "reliable and secure multishot network coding using linearized reed solomon codes"
    - "extended integrated interleaved codes over any field with applications to locally recoverable codes"
    - "random construction of partial mds codes"
    - "how long can optimal locally repairable codes be"
    - "constructions of maximally recoverable local reconstruction codes via function fields"
    - "locally repairable codes with unequal local erasure correction"
    - "optimal locally repairable codes of distance 3 and 4 via cyclic codes"

Connected through hyperedge HE-6 (induced by source paper "a tight rate bound and a matching construction for locally recoverable codes with sequential recovery from any number of multiple erasures"):
  with members:
    - "on minimum distance of locally repairable codes"
    - "binary codes with locality for multiple erasures having short block length"
    - "binary codes with locality for four erasures"
    - "codes with hierarchical locality"
    - "binary locally repairable codes sequential repair for multiple erasures"
    - "an upper bound on the minimum distance of ldpc codes over gf q"
    - "locally repairable codes with functional repair and multiple erasure tolerance"
    - "bounds on the parameters of locally recoverable codes"

Connected through hyperedge HE-7 (induced by source paper "matroid theory and storage codes bounds and constructions"):
  with members:
    - "locally recoverable codes from algebraic curves and surfaces"
    - "improved singleton type bounds for locally repairable codes"
    - "constructions and properties of linear locally repairable codes"
    - "codes with hierarchical locality"
    - "optimal binary locally repairable codes via anticodes"
    - "pir with low storage overhead coding instead of replication"
    - "bounds for batch codes with restricted query size"
    - "applications of polymatroid theory to distributed storage systems"

Connected through hyperedge HE-8 (induced by source paper "on optimal locally repairable codes with super linear length"):
  with members:
    - "combinatorial alphabet dependent bounds for locally recoverable codes"
    - "how long can optimal locally repairable codes be"
    - "explicit construction of optimal locally recoverable codes of distance 5 and 6 via binary constant weight codes"
    - "optimal lrc codes for all lenghts n q"
    - "optimal locally repairable codes of distance 3 and 4 via cyclic codes"
    - "explicit optimal length locally repairable codes of distance 5"
    - "irregular recovery and unequal locality for locally recoverable codes with availability"
    - "locality and availability of array codes constructed from subspaces"

Question: Please tell me which class the center node 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)