KATHRYN and her school friends have been using a Lorenz-type code to pass covert messages to each other. Each letter is expressed as a five-digit binary number such that A = 1 = 00001, M = 13 = 01101 and so on, but other symbols are represented by 00000 and by 11011 upwards.

A fixed letter, say M, is chosen as a “coder”, known only to the sender and receiver. To transmit a letter, say D, it is added to the coder by the “exclusive-NOR” rule 1 + 1 = 1, 1 + 0 = 0, 0 + 1 = 0, 0 + 0 = 1. So, for example, D + M = 00100 + 01101 = 10110 = V. When the sent letter V is added by the recipient to the coder M, the original letter reappears: 10110 + 01101 = 00100.

She has sent her name to her friends as seven letters. KATHRYN and its coded version together consist of 14 different letters.

What was the coded version?

Note: Adapted from Enigma Number:1764 by Adrian Sommerfield, which appered in the New Scientist on 28 August, 2013.