o---------o

JA:  If you interpret B = {0, 1} as a set of logical values
     in the usual way, that is, with 0 = false and 1 = true,
     then addition has the meaning of exclusive disjunction,
     and multiplication has the meaning of conjunction.

JA:  Galois Fields and other finite fields are widely
     employed in error-correcting codes these days,
     among many other places in applied maths.

JA:  Here begins your putative translation of L0 &amp; L1
     into 2-adic form.  If I understand you corr