Galois LCD Codes Over Fq + uFq + vFq + uvFq
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In <cit.>, Wu and Shi studied l-Galois LCD codes over finite chain ring ℛ=𝔽_q+u𝔽_q, where u^2=0 and q=p^e for some prime p and positive integer e. In this work, we extend the results to the finite non chain ring ℛ =𝔽_q+u𝔽_q+v𝔽_q+uv𝔽_q, where u^2=u,v^2=v and uv=vu. We define a correspondence between l-Galois dual of linear codes over ℛ and l-Galois dual of its component codes over 𝔽_q . Further, we construct Euclidean LCD and l-Galois LCD codes from linear code over ℛ. This consequently leads us to prove that any linear code over ℛ is equivalent to Euclidean (q>3) and l-Galois LCD (0<l<e, and p^e-l+1| p^e-1) code over ℛ . Finally, we investigate MDS codes over ℛ .
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