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On a class of constacyclic codes of length 4ps over Fpm + uFpm
(World Scientiﬁc Publishing Company DOI, 2017-12-24) Hai Q. Dinh; Bac T. Nguyen; Songsak Sriboonchitta
Present Let p be a prime such that pm ≡3 (mod 4). For any unit λ of Fpm , we determine the algebraic structures of λ-constacyclic codes of length 4ps over the ﬁnite commutative chain ring Fpm + uFpm , u2 = 0. If the unit λ ∈ Fpm is a square, each λ-constacycliccode of length 4ps is expressed as a direct sum of an -α-constacyclic code and an α constacyclic code of length 2ps. If the unit λ is not a square, then x4 −λ0 can bedecomposed into a product of two irreducible coprime quadratic polynomials which arex2 + γx + γ2 2 and x 2 −γx + γ2 2 , where λ ps 0 = λ and γ4 = −4λ0. By showing that thequotient rings ˙` R x2+γx+γ2 2 ´ps ¸ and nR˙`x2−γx+γ2 2 ´ps ¸ are local, non-chain rings, we can compute the number of codewords in each of λ-constacyclic codes. Moreover, the duals of such codes are also given.