Abstract |
The aim of this paper is to determine the algebraic structures of all λ-constacyclic codes of length 2 p s over the finite commutative chain ring F p m + u F p m , where p is an odd prime and u 2 = 0 . For this purpose, the situation of λ is mainly divided into two cases separately. If the unit λ is not a square and λ = α + u β for nonzero elements α , β of F p m , it is shown that the ambient ring ( F p m + u F p m ) x / { x 2 p s - ( α + u β ) } is a chain ring with the unique maximal ideal { x 2 - α 0 } , and thus ( α + u β ) -constacyclic codes are { ( x 2 - α 0 ) i } for 0 ≤ i ≤ 2 p s . If the unit λ is not a square and λ = γ for some nonzero element γ of F p m , such λ-constacyclic codes are classified into 4 distinct types of ideals. The detailed structures of ideals in each type are provided. Among other results, the number of codewords and the dual of every λ-constacyclic code are obtained.
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Recommended Citation |
Chen, Bocong; Dinh, Hai Q; Liu, Hongwei; Wang, Liqi (2016). Constacyclic codes of length 2ps over F p m + u F p m. Elsevier 37 108-130. doi: 10.1016/j.ffa.2015.09.006. Retrieved from https://oaks.kent.edu/mathpubs/16
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