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We present a construction of Hermitian operators and quantum states labelledby strings from a finite field. The distance between these operators or statesis then simply related (typically, proportional) to the Hamming distancebetween their corresponding strings. This allows a straightforward applicationof classical coding theory to find arrangements of operators or states with agiven distance distribution. Using the simplex or extended Reed-Solomon code inour construction recovers the discrete Wigner function, which has importantapplications in quantum information theory.

Classical codes in quantum state space