Generalized Singleton Type Upper Bounds

  title={Generalized Singleton Type Upper Bounds},
  author={Haoyuan Chen},



On Optimal Locally Repairable Codes with Super-Linear Length

Optimal locally repairable codes with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds both improve

Coordinate-Ordering-Free Upper Bounds for Linear Insertion-Deletion Codes

  • Hao Chen
  • Computer Science
    IEEE Transactions on Information Theory
  • 2022
Several coordinate-ordering-free upper bounds on the insdel distances of linear codes are proved, which are stronger than some previous known bounds.

A Note on Upper Bounds for Minimum Distance Codes

  • D. D. Joshi
  • Computer Science, Mathematics
    Inf. Control.
  • 1958

Linear Programming Bounds for Codes via a Covering Argument

The first linear programming bound of McEliece, Rodemich, Rumsey, and Welch for binary error-correcting codes and designs is recovered via a covering argument and is a natural isoperimetric constant of the Hamming cube, related to its Faber–Krahn minima.

Upper bounds on maximum lengths of Singleton-optimal locally repairable codes

This paper studies the problem for large range of parameters including the case where minimum distance is proportional to length and derives some upper bounds on the maximum length of Singleton-optimal locally repairable codes with small minimum distance by removing this constraint.

The Geometry of Two‐Weight Codes

On etudie les relations entre les codes [n,k] lineaires a deux poids, les ensembles (n,k,h 1 h 2 ) projectifs et certains graphes fortement reguliers

Good coverings of Hamming spaces with spheres

The Generalized Covering Radii of Linear Codes

A fundamental property of linear codes -- the generalized covering radius -- is suggested, which characterizes the trade-off between storage amount, latency, and access complexity, in database systems.

Codes From Difference Sets

Mathematical Foundations Linear Codes over Finite Fields Designs and Their Codes Difference Sets Almost Difference Sets Linear Codes of Difference Sets Linear Codes of Almost Difference Sets

Singleton-type bounds for list-decoding and list-recovery, and related results

A new Singleton-type upper bound for list-decodable codes is proved, which improves upon the previously known bound by roughly a factor of 1/L, and it is shown that for a wide range of parameters, list-Decodable nonlinear codes can strictly outperform list- decodable linear codes.