On the Gray images of some constacyclic codes over F p + u F p + u 2 F p
Tóm tắt
Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, a new Gray map between codes over F
p
+ u
F
p
+ u
2
F
p
and codes over F
p
is defined, where p is an odd prime. By means of this map, it is shown that the Gray image of a linear (1+u+u
2)-constacyclic code over F
p
+ u
F
p
+ u
2
F
p
of length n is a repeated-root cyclic code over F
p
of length pn. Furthermore, some examples of optimal linear cyclic codes over F
3 from (1 + u + u
2)-constacyclic codes over F
3 + u
F
3 + u
2
F
3 are given.
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