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Type I and Type II codes over the ring $𝔽_{2} + u 𝔽_{2} + v 𝔽_{2} + u v 𝔽_{2}$
- Ankur and
- Pramod Kumar Kewat
Asian-European Journal of Mathematics01 Apr 2019
Preview Abstract
We discuss self-dual codes over the ring $R_{u, v} = 𝔽_{2} + u 𝔽_{2} + v 𝔽_{2} + u v 𝔽_{2}, u^{2} = 0, v^{2} = 0, u v = v u$ . We characterize the structure of self-dual, Type I codes and Type II codes over $R_{u, v}$ with given generator matrix in terms of the structure of their Torsion and Residue codes. We construct self-dual, Type I and Type II codes over $R_{u, v}$ for different lengths.

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