#### Title

Constacyclic codes of length 2ps over F p m + u F p m

#### Publication Title

Finite Fields and Their Applications

#### Publication Date

1-2016

#### Document Type

Article

#### DOI

10.1016/j.ffa.2015.09.006

#### Keywords

94A55, 94B05, constacyclic codes, dual codes, repeated-root codes

#### Disciplines

Algebra | Applied Mathematics | Mathematics

#### 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.

#### Recommended Citation

Chen, Bocong; Dinh, Hai Q.; Liu, Hongwei; and Wang, Liqi (2016). Constacyclic codes of length 2ps over F p m + u F p m. *Finite Fields and Their Applications* 37, 108-130. doi: 10.1016/j.ffa.2015.09.006 Retrieved from https://digitalcommons.kent.edu/mathpubs/16

#### Publisher

Elsevier

#### Publisher Location

Amsterdam, Netherlands