“Coding theory and cryptography, the essentials” covering most of Chapters 1 through 6 as well as some parts of Chapters 11 and 12.

定义

parity matrix

技巧

1 column is not enough unless their is a column of all 0. 2 columns are not enough unless their is a repeated column

计算 parity matrix

如何根据parity matrix提取 codeword信息

Syndrome Decoding

根据parity matrix 解码

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标准型

Reed-Solomon codes

BCH-codes

汉明码

也就是说

汉明码(7,4) 只能纠错一位，多了会confuse

linear codes

A linear code C must contain the zero word.

the distance of a linear code is the weight of the nonzero code- word of least weight.

minimum distance

change one codeword to another requires at least d bit changes

If a code C has minimum distance d, then C can be used either to detect up to d-1 errors, or to correct up tp (d-1)/2 errors in any codeword. since any d − 1 transmission errors cannot change one codeword to another.

小例子