Algebraic decoding of the (32, 16, 8) quadratic residue code

An algebraic decoding algorithm for the 1/2-rate (32, 16, 8) quadratic residue (QR) code is found. The key idea of this algorithm is to find the error locator polynomial by a systematic use of the Newton identities associated with the code syndromes. The techniques developed extend the algebraic decoding algorithm found recently for the (32, 16, 8) QR code. It is expected that the algebraic approach developed here and by M. Elia (1987) applies also to longer QR codes and other BCH-type codes that are not fully decoded by the standard BCH decoding algorithm.<
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