Binomial moments of the distance distribution and the probability of undetected error

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In [1] K.A.S. Abdel-Ghaffar derives a lower bound on the probability of undetected error for unrestricted codes. The proof relies implicitly on the binomial moments of the distance distribution of the code. The authors use the fact that these moments count the size of subcodes of the code to give a very simple proof of the bound in [1] by showing that it is essentially equivalent to the Singleton bound. They discuss some combinatorial connections revealed by this proof. They also discuss some improvements of this bound. Finally, they analyze asymptotics. They show that an upper bound on the undetected ... continued below

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7 p.

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Barg, A. & Ashikhmin, A. September 1, 1998.

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  • Barg, A. Lucent Technologies, Murray Hill, NJ (United States). Bell Labs.
  • Ashikhmin, A. Los Alamos National Lab., NM (United States)

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Description

In [1] K.A.S. Abdel-Ghaffar derives a lower bound on the probability of undetected error for unrestricted codes. The proof relies implicitly on the binomial moments of the distance distribution of the code. The authors use the fact that these moments count the size of subcodes of the code to give a very simple proof of the bound in [1] by showing that it is essentially equivalent to the Singleton bound. They discuss some combinatorial connections revealed by this proof. They also discuss some improvements of this bound. Finally, they analyze asymptotics. They show that an upper bound on the undetected error exponent that corresponds to the bound of [1] improves known bounds on this function.

Physical Description

7 p.

Notes

OSTI as DE98006315

Source

  • International coding theory, Cd de Guanajuato (Mexico), 20-24 Apr 1998

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  • Other: DE98006315
  • Report No.: LA-UR--98-868
  • Report No.: CONF-980463--
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 677090
  • Archival Resource Key: ark:/67531/metadc711330

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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Creation Date

  • September 1, 1998

Added to The UNT Digital Library

  • Sept. 12, 2015, 6:31 a.m.

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  • May 5, 2016, 6:18 p.m.

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Barg, A. & Ashikhmin, A. Binomial moments of the distance distribution and the probability of undetected error, article, September 1, 1998; New Mexico. (digital.library.unt.edu/ark:/67531/metadc711330/: accessed December 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.