Let p be any prime, s and m be positive integers. In this paper, we completely determine the Hamming distance of all constacyclic codes of length p s over the finite commutative chain ring F p m + uF p m + u 2 F p m (u 3 = 0). As applications, we identify all maximum distance saparable codes (i.e., optimal codes with respect to the Singleton bound) among them.
INDEX TERMSHamming distance; constacyclic codes; optimal codes; MDS codes.
Let p be a prime, s, m be positive integers, γ be a nonzero element of the finite field Fpm, and let R=Fpm[u]/⟨u3⟩ be the finite commutative chain ring. In this paper, the symbol-pair distances of all γ-constacyclic codes of length ps over R are completely determined.
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