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##### Maximum Distance Separable b-Symbol Repeated-Root γ-Constacylic Codes over a Finite Chain Ring of Length 2

**Authors:**
Jamal Laaouine,
Mohammed Elhassani Charkani

**Abstract:**

Let p be a prime and let b be an integer. MDS b-symbol codes are a direct generalization of MDS codes. The γ-constacyclic codes of length pˢ over the finite commutative chain ring Fₚm [u]/ < u² > had been classified into four distinct types, where is a nonzero element of the field Fₚm. Let C₃ be a code of Type 3. In this paper, we obtain the b-symbol distance db(C₃) of the code C₃. Using this result, necessary and sufficient conditions under which C₃ is an MDS b-symbol code are given.

**Keywords:**
constacyclic code,
repeated-root code,
maximum distance separable,
MDS codes,
b-symbol distance,
finite chain rings

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