Abstract
This paper presents majority-decoding algorithms for four classes of binary cyclic codes. The classes are those for which the parity-check polynomial is: 1) the product of two primitive polynomials with relatively prime exponents and 2) the product of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(x^r + 1)/(x + 1)</tex> and a primitive polynomial, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r \geq 3</tex> is odd and the exponents are relatively prime, together with the corresponding nonexpurgated codes.
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