On a class of constacyclic codes of length 4 ps over pm + upm

• Main Authors: Hai Q. Dinh, Bac T. Nguyen, Songsak Sriboonchitta, Thang M. Vo
• Format: Journal
• Published: 2019
• Subjects: Mathematics
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85059046776&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/63683
• Institution: Chiang Mai University

© 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.