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==Decoding Barcode Algorithm Calculation== ===Design=== *Based on Gunderson article in Genome Research (2004) "Decoding Randomly Ordered DNA Arrays" **Use multiple stages (cycles) of 2 or 3 dyes **Every barcode should have 2 blank stages for error correction ***Most common error is color -> blank or blank -> color (color1 -> color2 is very unlikely) ***Therefore if a common error occurs it will be easy to recognize and discard because will have greater than or fewer than 2 blank stages **Last caveat: No barcode can have the same color for all cycles ===Calculate Number of Unique Barcodes=== *With 7 stages of 3 dyes with 2 blank stages *First ignore the blank stages and only consider the 5 colored stages **3^5=243 is the number of permutations(combinations) *Next consider all the possible positions where the pair of blanks could be **This is the combination 7 choose 2 = 6+5+4+3+2+1 = 21 ***ie. 1&2, 1&3, 1&4, ...,1&7, 2&3, 2&4, ..., 6&7 *Combining the 5 color stages with the 2 blank stages **3^5 x 21 = 5,103 *Finally we must remove any barcodes where every color stage is the same color (e.g. Red,0,Red,Red,Red,0,Red) **For each of the 3 colors there are 21 of these barcodes (all the possible combinations of where the blank stages are) **Therefore there are 3 x 21 = 63 barcodes with only one color *'''Result:''' 3^5 x 21 - 3 x 21 = 5,040 Unique Barcodes
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