# Extended Binomial Moments of a Linear Code and the Undetected Error Probability

Extended Binomial Moments of a Linear Code and the Undetected Error Probability Extended binomial moments of a linear code, introduced in this paper, are synonymously related to the code weight distribution and linearly to its binomial moments. In contrast to the latter, the extended binomial moments are monotone, which makes them appropriate for studying the undetected error probability. We establish some properties of the extended binomial moments and, based on this, derive new lower and upper bounds on the probability of undetected error. Also, we give a simplification of some previously obtained sufficient conditions for proper and good codes, stated in terms of the extended binomial moments. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# Extended Binomial Moments of a Linear Code and the Undetected Error Probability

, Volume 39 (3) – Oct 3, 2004
11 pages

/lp/springer_journal/extended-binomial-moments-of-a-linear-code-and-the-undetected-error-do2STf7EWz
Publisher
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1023/A:1026162531539
Publisher site
See Article on Publisher Site

### Abstract

Extended binomial moments of a linear code, introduced in this paper, are synonymously related to the code weight distribution and linearly to its binomial moments. In contrast to the latter, the extended binomial moments are monotone, which makes them appropriate for studying the undetected error probability. We establish some properties of the extended binomial moments and, based on this, derive new lower and upper bounds on the probability of undetected error. Also, we give a simplification of some previously obtained sufficient conditions for proper and good codes, stated in terms of the extended binomial moments.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 3, 2004

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