A system that produces one or more non-repeating randomizer sequences of
up to 2.sup.m-1 or more m-bit symbols includes a randomizer circuit that
is set up in accordance with a polynomial with primitive elements of
GF(2.sup.m) as coefficients. The system combines the randomizer sequence
with all the symbols of ECC code words that are encoded using a BCH code
over GF(2.sup.m) to produce a randomized code word. The particular
primitive elements used and/or an initial state of one or more registers
in the system specifies the particular sequence produced by the system.
The initial state of each of the one or more registers is a selected one
of the 2.sup.m-1 elements of GF(2.sup.m), and thus, 2.sup.m-1 different
sequences may be produced by selecting a different initial state for a
given one of the registers. If the coefficients are also selected from,
for example, a set of "p" possible values, the system produces
p*(2.sup.m-1) different sequences. The system may thus be used to encrypt
the ECC code word by associating the code word with a particular selected
initial state and/or coefficient. The coefficients may be selected to
produce randomizer sequences that are predetermined minimum distances
away from both the ECC code words.