← ToolBox / 汉明距离估算

📏 Hamming Distance Estimator

Estimate the differing-bit count of two equal-length binary strings for error-correction and link-reliability analysis.

二进制串长度

差异比特比例 %

采样数

汉明距离（本页为估算口径，非逐位比较实现）：估算差异比特数 = round(串长 × 差异率% ÷ 100)；采样差异 = round(采样数 × 差异率% ÷ 100)。校验：无强校验，空值按 0 兜底。判据：无固定分级，按差异率线性估算、四舍五入取整，串长与采样数各自独立折算。

差异率可用采样统计近似。

📚 深度解析：汉明距离估算

示例：10110 与 10011

逐位比较第 3、5 位不同，汉明距离 = 2，可检 1 位错但不足以纠 1 位（需距离≥3）。

Item	Formula / Rule	Source / Standard
Hamming distance	d(x, y) = popcount(x XOR y), the number of differing bits	Hamming, Error Detecting and Error Correcting Codes, 1950
Correction criterion	Correcting t bits needs d ≥ 2t + 1; detecting e bits needs d ≥ e + 1	Hamming 1950 §2 Minimum distance bound
Normalized distance	Normalized distance = d(x, y) / n over n-bit codewords, ranging from 0 to 1	ISO/IEC 2382 Information technology vocabulary