  This paper proposes a novel algorithm for finding error-locators of
algebraic-geometric codes that can eliminate the division-calculations of
finite fields from the Berlekamp-Massey-Sakata algorithm. This inverse-free
algorithm provides full performance in correcting a certain class of errors,
generic errors, which includes most errors, and can decode codes on algebraic
curves without the determination of unknown syndromes. Moreover, we propose
three different kinds of architectures that our algorithm can be applied to,
and we represent the control operation of shift-registers and switches at each
clock-timing with numerical simulations. We estimate the performance in
comparison of the total running time and the numbers of multipliers and
shift-registers in three architectures with those of the conventional ones for
codes on algebraic curves.
