Computational Discrete Mathematics

One recent direction in coding theory has been to study linear codes over the alphabet Z4 and apply the Gray map from Z4 to binary pairs to obtain binary nonlinear codes better than comparable binary linear codes. This connection between linear codes over Z4 and nonlinear binary codes was also the breakthrough in solving an old puzzle of the apparent duality between the nonlinear Kerdock and Preparata codes. We present a description of this puzzle and a brief introduction to codes over Z4.

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