The probability of undetected error P/sub u/( epsilon ) for the primitive triple-error-correcting BCH codes of blocklength 2/sup m/-1 used solely for error detection on a binary symmetric channel with crossover probability epsilon >or=1/2 is examined. It is shown that for odd values of m, P/sub u/( epsilon ) increases monotonically with epsilon . For even values of m, this is not necessarily true. However, for a fixed epsilon , as m increases, P/sub u/( epsilon ) approaches 2/sup -p/, where p is the number of parity bits. Similar characteristics are exhibited by the extended codes.
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机译：原始长度为3 / sup m / -1的原始三重纠错BCH码未检测到的错误P / sub u /（epsilon）的概率仅用于交叉概率epsilon> or = 1的二进制对称信道上的错误检测/ 2被检查。结果表明，对于m的奇数值，P / sub u /（epsilon）与epsilon单调增加。对于偶数的m，这不一定是正确的。但是，对于固定的ε，随着m的增加，P / sub u /（epsilon）接近2 / sup -p /，其中p是奇偶校验位的数量。扩展代码显示出相似的特性。
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