Numerical Results on the Asymptotic Rate of Binary Codes (2007)
Barg And David, A. Barg, David B. Jaffe
. We compute upper bounds on the maximal size of a binary linear code of length n 1000, dimension k, and distance d For each value of d, the bound is found by solving the Delsarte linear programming...
Polynomial method in coding and information theory (1999)
Ashikhmin, A., Barg, A., Litsyn, S.
Polynomial, or Delsarte's, method in coding theory accounts for a variety of structural results on, and bounds on the size of, extremal configurations (codes and designs) in various metric spaces. In...
Quantum Error Detection II: Bounds (1999)
Ashikhmin, A., Barg, A., Knill, E., Litsyn, S.
In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower (existence) bound...
A new upper bound on the reliability function of the Gaussian channel (1999)
A. Ashikhmin, A. Barg, S. Litsyn
We derive a new upper bound on the exponent of error probability of decoding for the best possible codes in the Gaussian channel. This bound is tighter than the known upper bounds (the sphere-packing...
A New Upper Bound on Codes Decodable Into Size-2 Lists (1999)
A. Ashikhmin, A. Barg, S. Litsyn
A new asymptotic upper bound on the size of binary codes with the property described in the title is derived. The proof relies on the properties of the distance distribution of binary codes...
New Upper Bounds on Generalized Weights (1998)
A. Ashikhmin, A. Barg, S. Litsyn
We derive new asymptotic upper bounds on the generalized weights of a binary linear code of a given size. We also prove some asymptotic results on the distance distribution of binary codes. 1...