Extended binomial moments of a linear code and the undetected error probability

Abstract

The 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 very appropriate for study of the undetected error probability. In this work we establish some properties of the extended binomial moments and based on this we 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