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Adding an overall parity-check digit to a quadratic residue code gives an extended quadratic residue code. When p ≡ 3 {\displaystyle p\equiv 3} (mod 4 {\displaystyle 4} ) an extended quadratic residue code is self-dual; otherwise it is equivalent but not equal to its dual.
One of MacWilliams' significant achievements was her encyclopedic book, The Theory of Error-Correcting Codes, which she wrote in collaboration with Neil Sloane [1] [8] and was published in 1977. The book is stated as being "Perhaps the most comprehensive text on the algebraic and combinatorial properties of error-correcting codes, and of ...
Download as PDF; Printable version; ... The upcoming wireless 5G standard raises a new range of applications ... The Theory of Error-Correcting Codes. North-Holland ...
A special case of constant weight codes are the one-of-N codes, that encode bits in a code-word of bits. The one-of-two code uses the code words 01 and 10 to encode the bits '0' and '1'. A one-of-four code can use the words 0001, 0010, 0100, 1000 in order to encode two bits 00, 01, 10, and 11.
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Linear block codes have the property of linearity, i.e. the sum of any two codewords is also a code word, and they are applied to the source bits in blocks, hence the name linear block codes. There are block codes that are not linear, but it is difficult to prove that a code is a good one without this property.
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