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In this paper, we study the algebraic structure of Z2 [u]Z2 [u, v]-additive codes which are Z2 [u, v]-submodules where u2 = v2 = 0 and uv = vu. In particular, we determine a Gray map from Z2[u]Z2[u, v] to Z22&#x03B1;+8&#x03B2; and study generator and parity check matrices for these codes. Further we study the structure of Z2[u]Z2[u, v]-additive cyclic codes.

The structure of Z2[u]Z2[u, v]-additive Codes