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✅ Hamming Code Parity Bits

Compute the Hamming parity bits r from data bits m using 2^r >= m + r + 1 for single-bit error correction.

数据位数

消息数据位总数

传输速率 bit/s

满足 2ʳ ≥ m + r + 1 的最小 r
码长 = m + r，效率 = m/(m+r)

汉明码可检测并纠正单比特错误。

📚 深度解析：汉明码校验位

示例：8 位数据

需 r=4（2^4=16≥8+4+1=13），共 12 位码字，可纠 1 位错、检 2 位错。

Item	Formula / Rule	Source / Standard
Parity bit count	Requires 2^k ≥ m + k + 1 with m data bits and k parity bits	Hamming, Error Detecting and Error Correcting Codes, 1950
Correction capability	With distance d = 3 the code corrects t = ⌊(d − 1)/2⌋ = 1 bit and detects 2	Hamming 1950 §3 Single-error-correcting code
Codeword length	n = m + k, with parity bits placed at power-of-two positions 1, 2, 4, 8, …	ISO/IEC 2382 Information technology vocabulary