A new method we introduced recently for constructing linear codes from algebraic curves is reviewed. The construction of a new class of double-error-correcting codes from Hermitian curves is presented in detail. These double-error-correcting codes are shown to have better code rate compared to the algebraic-geometric Hermitian codes of the same length. It is then shown that the decoding of these codes can be accomplished using two runs of the Berlekamp-Massey algorithm.
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