Some inequalities concerning binomial coefficients and the weight distribution of proper linear codes

Authors:
H. D. Wacker;J. Boercsoek
Affiliations:
Development, HIMA Paul Hildebrandt GmbH + Co KG, Bruehl, Germany;Development, HIMA Paul Hildebrandt GmbH + Co KG, Bruehl, Germany
Venue:
ACS'07 Proceedings of the 7th Conference on 7th WSEAS International Conference on Applied Computer Science - Volume 7
Year:
2007

Citing 5
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Abstract

Proper linear codes play an important role in error detection. They are characterized by an increasing probability of undetected error pue(ε, C) and are considered "good for error detection". A lot of CRCs commonly used to protect data transmission via a variety of field busses are known for being proper. In this paper the weight distribution of proper linear codes on a binary symmetric channel without memory is investigated. A proof is given that its components are upper bounded by the binomial coefficients in a certain sense. Secondly an upper bound of the tail of the binomial is given, and the results are then used to derive estimates of pue(ε, C). Finally, applications on safety integrity levels are studied.