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Title: On a class of constacyclic codes of length 4 ps over pm + upm
Authors: Hai Q. Dinh
Bac T. Nguyen
Songsak Sriboonchitta
Thang M. Vo
Keywords: Mathematics
Issue Date: 1-Feb-2019
Abstract: © 2019 World Scientific Publishing Company. Let p be a prime such that pm ≡ 3(mod 4). For any unit λ of pm, we determine the algebraic structures of λ-constacyclic codes of length 4ps over the finite commutative chain ring pm + upm, u2 = 0. If the unit λ pm is a square, each λ-constacyclic code 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 - λ 0 can be decomposed into a product of two irreducible coprime quadratic polynomials which are x2 + γx + γ2 2 and x2 - γx + γ2 2, where λ0ps = λ and γ4 = -4λ 0. By showing that the quotient rings ℝ x2+γx+γ2 2 ps and ℝ 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.
ISSN: 02194988
Appears in Collections:CMUL: Journal Articles

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