A general family of Plotkin-optimal two-weight codes over ℤ_4

07/30/2022

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by   Hopein Christofen Tang, et al.

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We obtained all possible parameters of Plotkin-optimal two-Lee weight projective codes over ℤ_4, together with their weight distributions. We show the existence of codes with these parameters as well as their weight distributions by constructing an infinite family of two-weight codes. Previously known codes constructed by Shi et al. (Des Codes Cryptogr. 88(3):1-13, 2020) can be derived as a special case of our results. We also prove that the Gray image of any Plotkin-optimal two-Lee weight projective codes over ℤ_4 has the same parameters and weight distribution as some two-weight binary projective codes of type SU1 in the sense of Calderbank and Kantor (Bull. Lond. Math. Soc. 18:97-122, 1986).