IT is known that the average undetected error probability （UEP） of a binary [n, k] code Con a binary symmetric channel with crossover probability p is given byP<sub>e</sub>（p） = sum from i=1 A<sub&g...IT is known that the average undetected error probability （UEP） of a binary [n, k] code Con a binary symmetric channel with crossover probability p is given byP<sub>e</sub>（p） = sum from i=1 A<sub>i</sub>p<sup>i</sup>（1-p）<sup>n-1</sup>, （1）where （A<sub>0</sub>, A<sub>1</sub>,…, A<sub>n</sub>） is the weight distribution of C. If for all 0≤p≤0.5, P<sub>e</sub>（p）≤P<sub>e</sub>（0. 5） = 2<sup>k-n</sup>-2<sup>-n</sup>, then C is called good for error detection. Moreover, if P<sub>e</sub> （p） ismonotonously increasing in the interval [0, 0.5], then C is called proper. Clearly, propercodes are good.展开更多
文摘IT is known that the average undetected error probability （UEP） of a binary [n, k] code Con a binary symmetric channel with crossover probability p is given byP<sub>e</sub>（p） = sum from i=1 A<sub>i</sub>p<sup>i</sup>（1-p）<sup>n-1</sup>, （1）where （A<sub>0</sub>, A<sub>1</sub>,…, A<sub>n</sub>） is the weight distribution of C. If for all 0≤p≤0.5, P<sub>e</sub>（p）≤P<sub>e</sub>（0. 5） = 2<sup>k-n</sup>-2<sup>-n</sup>, then C is called good for error detection. Moreover, if P<sub>e</sub> （p） ismonotonously increasing in the interval [0, 0.5], then C is called proper. Clearly, propercodes are good.
