The algebraic structure of additive codes over 𝔽2𝔽8

Abstract

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