On some properties of the undetected error probability of linear codes (Corresp.)
- 1 January 1979
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 25 (1) , 110-112
- https://doi.org/10.1109/tit.1979.1055991
Abstract
A recent paper [1] discussed the2^{-p}bound (wherep = n- k) for the probability of undetected errorP(\epsilon)for an(n,k)block code used for error detection on a binary symmetric channel. This investigation is continued and extended and dual codes are studied. The dual and extension of a perfect code obey the2^{-p}bound, but this is not necessarily true for arbitrary codes that obey the bound. Double-error-correcting BCH codes are shown to obey the bound. Finally the problem of constructing uniformly good codes is examined.Keywords
This publication has 3 references indexed in Scilit:
- Concerning a bound on undetected error probability (Corresp.)IEEE Transactions on Information Theory, 1976
- On the Nonexistence of Perfect Codes over Finite FieldsSIAM Journal on Applied Mathematics, 1973
- A Theorem on the Distribution of Weights in a Systematic Code†Bell System Technical Journal, 1963