Quantum Codes from (1-2w-2uv)-Constacyclic Codes over the F_q+uF_q+vF_q+wF_q+uvF_q

Abstract

In this paper, we give construction of quantum codes over 𝔽 𝑞 from (1 − 2𝑤 − 2𝑢𝑣) -constacyclic codes over the 𝔽 𝑞 + 𝑢𝔽 𝑞 + 𝑣𝔽 𝑞 + 𝑤𝔽 𝑞 + 𝑢𝑣𝔽 𝑞 , where 𝑢 2 = 𝑢, 𝑣 2 = 𝑣, 𝑤 2 = 𝑤, 𝑢𝑣 = 𝑣𝑢, 𝑢𝑤 = 𝑤𝑢 = 𝑣𝑤 = 𝑤𝑣 = 0, 𝑞 = 𝑝 𝑚 , 𝑚 is a positive integer and 𝑝 is an odd prime. We determine the parameters of quantum error correcting codes which constructed from (1 − 2𝑤 − 2𝑢𝑣) -constacyclic codes over the 𝔽 𝑞 + 𝑢𝔽 𝑞 + 𝑣𝔽 𝑞 + 𝑤𝔽 𝑞 + 𝑢𝑣𝔽 𝑞 .