In this paper, we explore some properties of hulls of cyclic serial codes over a finite chain ring and we provide an algorithm for computing all the possible parameters of the Euclidean hulls of that codes. We also establish the average p r -dimension of the Euclidean hull, where F p r is the residue field of R, as well as we give some results of its relative growth.
Let R be a finite principal ideal ring and S the Galois extension of R of degree m. For k and k ′ , positive integers we determine the number of free S-linear codes B of length ℓ with the property k = rank S (B) and k ′ = rank R (B ∩ R ℓ ). This corrects a wrong result [1, Theorem 6] which was given in the case of finite fields.
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