On symbol-triple distance of a class of constacyclic codes of length 3ps over Fpm + uFpm

Let p ≠ 3 be any prime. In this paper, we completely determine symbol-triple distance of all γ-constacyclic codes of length 3 p s over the finite commutative chain ring R = F p m + u F p m , where γ is a unit of R which is not a cube in F p m . We give the necessary and sufficient condition for a sy...

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Bibliographic Details
Published inIEEE access Vol. 11; p. 1
Main Authors Dinh, Hai Q., Nguyen, Bac T, Thi, Hiep L, Yamaka, Woraphon
Format Journal Article
LanguageEnglish
Published IEEE 15.02.2023
Subjects
chain rings
Codes
Constacyclic codes
dual codes
Encoding
Generators
Hamming distances
Linear codes
MDS symbol-triple codes
Measurement
symbol-triple codes
Symbols
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Summary:Let p ≠ 3 be any prime. In this paper, we completely determine symbol-triple distance of all γ-constacyclic codes of length 3 p s over the finite commutative chain ring R = F p m + u F p m , where γ is a unit of R which is not a cube in F p m . We give the necessary and sufficient condition for a symbol-triple γ-constacyclic code to be an MDS symbol-triple code. Using that, we establish all MDS symbol-triple γ-constacyclic codes of length 3 p s over R . Some examples of the symbol-triple distance of γ-constacyclic codes of length 3 p s over R are provided. We also list some new MDS symbol-triple γ-constacyclic codes of length 3 p s over R , where γ is not a cube in F p m .
ISSN:2169-3536
DOI:10.1109/ACCESS.2023.3245520