Abstract:A new Gray map is defined from R=F2+uF2+u2F2+u3F2 to F42 with u4=0. It is proved that the Gray image of a linear (1+u+u2+u3)-cyclic code of length n over R is a distance-invariant linear cyclic code of length 4n over F2 . Further more, the generator polynomials of the Gray image of this constacyclic code for odd length over R is determined, some optimal binary linear cyclic codes are also obtained.
王立启, 朱士信. 环F2[u]/(u4)上的一类常循环码及其Gray象[J]. 电子与信息学报, 2013, 35(2): 499-503.
Wang Li-Qi, Zhu Shi-Xin. A Class of Constacyclic Codes Over F2[u]/(u4) and Its Gray Image. , 2013, 35(2): 499-503.