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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

Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad 826 004, India

E-mail Address: ankuriitm@am.ism.ac.in

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and

Pramod Kumar Kewat

Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad 826 004, India

E-mail Address: kewat.pk.am@ismdhanbad.ac.in

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https://doi.org/10.1142/S1793557119500256Cited by:3 (Source: Crossref)

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.

Communicated by B. K. Dass

Keywords:

AMSC: 94B05

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