A [45, 13] Code with Minimal Distance 16


J.H. Conway
S.J. Lomonaco, Jr.
N.J.A. Sloane


A record code of length 45, dimension 13 and minimal distance 16 is constructed in several ways: as an Abelian code (an ideal in the regular representation of  C3 X C15) , from a  [15,6,8]  cyclic code over  GF(4) , and from the  | a+x | b+x | c+x |  construction. Its automorphism group has order 360, and its even sucode is a  [45,12,16]  code with only four nonzero weights.