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Motivated by the works of Shiromoto [3] and Shi et al. [4], we study theexistence of MacWilliams type identities with respect to Lee and Euclideanweight enumerators for linear codes over $\mathbb{Z}_{\ell}.$ Necessary andsufficient conditions for the existence of MacWilliams type identities withrespect to Lee and Euclidean weight enumerators for linear codes over$\mathbb{Z}_{\ell}$ are given. Some examples about such MacWilliams typeidentities are also presented.

MacWilliams type identities on the Lee and Euclidean weights for linear codes over $\mathbb{Z}_{\ell}$