Nonlinear codes from modified Butson–Hadamard matrices

Let $p\geq 3$ be a prime number. In this paper we construct two families of nonlinear $p$-ary codes derived from the corresponding families of modified Butson–Hadamard matrices. These codes have the minimal distances close to the Plotkin bound and very easy construction and decoding procedures. Moreover, for some of these codes the Plotkin bound is attained.