Author(s) | |
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Abstract |
For any prime p, all constacyclic codes of length ps over the ring ℛ = Fpm + uFpm are considered. The units of the ring ℛ are of the forms γ and ⍺ + uβ, where ⍺, β, and γ are nonzero elements of Fpm, which provides pm (pm -1) such constacyclic codes. First, the structure and Hamming distances of all constacyclic codes of length ps over the finite field Fpm are obtained; they are used as a tool to establish the structure and Hamming distances of all (⍺ + uβ)-constacyclic codes of length ps over ℛ. We then classify all cyclic codes of length ps over ℛ and obtain the number of codewords in each of those cyclic codes. Finally, a one-to-one correspondence between cyclic and γ-constacyclic codes of length ps over ℛ is constructed via ring isomorphism, which carries over the results regarding cyclic codes corresponding to γ-constacyclic codes of length ps over ℛ. |
Format | |
Identifier(s) | |
Publication Date |
2010-09-01
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Publication Title |
Elsevier
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Volume |
324
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Issue |
5
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First Page |
940
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Last Page |
950
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Keywords | |
Subject | |
Rights |
http://rightsstatements.org/vocab/InC/1.0/
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Community | |
Permalink | https://oaks.kent.edu/mathpubs/20 |
Dinh, H. (2010). Constacyclic Codes of Length p^s Over Fpm + uFpm (1–). Elsevier. https://doi.org/10.1016/J.JALGEBRA.2010.05.027
Dinh, Hai. 2010. “Constacyclic Codes of Length p^s Over Fpm + UFpm”. Elsevier. https://doi.org/10.1016/J.JALGEBRA.2010.05.027.
Dinh, Hai. Constacyclic Codes of Length p^s Over Fpm + UFpm. Elsevier, 1 Sept. 2010, https://doi.org/10.1016/J.JALGEBRA.2010.05.027.