Algebraic decoding of the (23,12,7) Golay code
IEEE Transactions on Information Theory
Decoding the (47,24,11) quadratic residue code
IEEE Transactions on Information Theory
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The algebraic decoding of binary quadratic residue codes can be performed using the Peterson or the Berlekamp-Massey algorithm once certain unknown syndromes are determined or eliminated. The technique of determining unknown syndromes is applied to the nonbinary case to decode the expurgated ternary quadratic residue code of length 23.