A Class of Constacyclic Codes OverF2[u]/(u4)and Its Gray Image

A new Gray map is defined fromR=F2+uF2+u2F2+u3F2 toF42 with u4=0. It is proved that the Gray image of a linear (1+u+u2+u3)-cyclic code of lengthn over R is a distance-invariant linear cyclic code of length4n over F2. Further more, the generator polynomials of the Gray image of this constacyclic code for odd length over Ris determined, some optimal binary linear cyclic codes are also obtained.