The algebraic structure of additive codes over 28.

In this paper, we investigate the algebraic structure of 2 r 8 s -additive codes, where r and s are nonnegative integers, 2 (respectively, 8 ) denotes the finite field of order 2 (respectively, 8). We first give the generator polynomials of additive cyclic codes over 8 and then the generator polynomials of additive cyclic codes over 2 8 is also given. In addition, we introduce a linear map W : 2 8 → 2 , and study its properties. What's more, the dual of additive cyclic codes over 2 8 are investigated as well. And we get that the duals of any additive cyclic codes over 2 8 are also additive cyclic codes. Finally, separable 2 8 -additive cyclic codes are investigated. [ABSTRACT FROM AUTHOR]