A new family of nonlinear codes, called weak flip codes, is presented and is shown to
contain many beautiful properties. In particular, the subfamily of fair weak flip codes can be
seen as a generalization of linear codes. Different from linear codes that only exist for a
number of codewords M being an integer-power of 2, the fair weak flip code can be defined
for an arbitrary M. It is then noted that the fair weak flip codes are related to binary nonlinear
Hadamard codes: both code families maximize the minimum Hamming distance and meet …

A new family of nonlinear codes, called weak flip codes, is presented and is shown to
contain many beautiful properties. In particular, the subfamily of fair weak flip codes can be
seen as a generalization of linear codes, ie, they possess some quasi-linear properties.
Different from linear codes that only exist for a number of codewords M being an integer-
power of 2, the fair weak flip code can be defined for an arbitrary M. It is then noted that the
fair weak flip codes are related to binary nonlinear Hadamard codes: both code families …