MacWilliams type identities on the Lee and Euclidean weights for linear codes over [formula omitted].

Motivated by the works of Shiromoto [3] and Shi et al. [4] , we study the existence of the MacWilliams type identities with respect to the Lee and Euclidean weight enumerators for linear codes over the ring Z ℓ . Necessary and sufficient conditions for the existence of the MacWilliams type identities with respect to the Lee and Euclidean weight enumerators for linear codes over Z ℓ are given. Some examples about such MacWilliams type identities are also presented. [ABSTRACT FROM AUTHOR]