Counting ℤ₂ℤ₄-Additive Codes

Counting Z2 Z4 Z8-additive Codes

“…In (6), if we replace κ = k 0 , δ = k 1 and γ − κ = k 2 , then it is obtained the number of Z 2 Z 4 -additive codes C of type (α, β; γ, δ, κ) as in [8], (Theorem 3.3).…”

“…They showed that all these binary codes are group-isomorphic to subgroups of Z α 2 × Z β 4 × Q σ 8 , being Q 8 the non-abelian quaternion group with eight elements. Recently, in particular, Z 2 Z 4 -additive codes and Z 2 Z 4 Z 8 -additive codes, which are a generalization of Z 2 Z 4 -additive codes, have been extensively studied [1][2][3][4][5][6]8].…”

“…Recently, in this regard, there has been some researches of particular types over the different rings. For example, while Dougherty et al [8] counted the Z 2 Z 4 -additive codes, Aydogdu et al [3] performed the count of the Z 2 Z 8 -additive codes. In this paper, we aim to focus on the number of matrices that generate different (not necessarily equivalent) Z 2 Z 4 Z 8 -additive codes.…”