  Inspired by the paper on quantum knots and knot mosaics [23] and grid
diagrams (or arc presentations), used extensively in the computations of
Heegaard-Floer knot homology [2,3,7,24], we construct the more concise
representation of knot mosaics and grid diagrams via mirror-curves. Tame knot
theory is equivalent to knot mosaics [23], mirror-curves, and grid diagrams
[3,7,22,24]. Hence, we introduce codes for mirror-curves treated as knot or
link diagrams placed in rectangular square grids, suitable for software
implementation. We provide tables of minimal mirror-curve codes for knots and
links obtained from rectangular grids of size 3x3 and px2 (p<5), and describe
an efficient algorithm for computing the Kauffman bracket and L-polynomials
[18,19,20] directly from mirror-curve representations.
