1. An error correction method of decoding a received codeword to obtain coefficients of a locator polynomial, said method comprising the steps of: (1) initializing a plurality of coefficient registers and loading a multiplicative identity field element expressed in a second basis representation into a first one of said coefficient registers; (2) loading syndrome values expressed in a first basis representation into appropriate ones of a plurality of syndrome registers; (3) using the contents of said coefficient registers and the contents of said syndrome registers to obtain a current discrepancy dn expressed in said second basis representation; (4) obtaining a quantity related to a multiplicative inverse d.sub.m.sup.-1 of a prior discrepancy d.sub.m, said quantity related to said multiplicative inverse d.sub.m.sup.-1 being expressed in said second basis representation; (5) multiplying said current discrepancy d.sub.n by said quantity related to said multiplicative inverse d.sub.m.sup.-1 to obtain a discrepancy product d.sub.n d.sub.m-1 ; (6) converting the contents of a plurality of said coefficient registers from said second basis representation to said first basis representation; (7) multiplying the converted contents of certain ones of said plurality of coefficient registers by the discrepancy product d.sub.n d.sub.m.sup.-1 to obtain a plurality of successions of products; (8) accumulating related ones of said products successively obtained in step (7) and loading said accumulations into appropriate ones of said coefficient registers.