Affine 3-nonsystematic perfect codes of length 15
S. A. Malyugin · Journal of Applied and Industrial Mathematics · 2015
A perfect binary code C of length n = 2 k − 1 is called affine 3-systematic if some 3-dimensional subspace L exists in the space {0, 1} n such that the intersection of each of its cosets L + u with C is either empty or a singleton. Otherwise, the code C is called affine 3-nonsystematic. In the paper, we construct four nonequivalent affine 3-nonsystematic codes of length 15 and study the properties of the complement {0, 1} n \ (C + C).