On (α + u β) constacyclic codes of length 4ps over Fpm + uFpm
© 2019 World Scientific Publishing Company. For any odd prime p such that pm ≡ 3(mod 4), the structures of all (α+uβ)-constacyclic codes of length 4ps over the finite commutative chain ring pm + upm (u2 = 0) are established in term of their generator polynomials. When the unit (α + uβ) is a square,...
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| Main Authors: | , , , |
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| Format: | Journal |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85059046681&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/63684 |
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| Institution: | Chiang Mai University |
| Summary: | © 2019 World Scientific Publishing Company. For any odd prime p such that pm ≡ 3(mod 4), the structures of all (α+uβ)-constacyclic codes of length 4ps over the finite commutative chain ring pm + upm (u2 = 0) are established in term of their generator polynomials. When the unit (α + uβ) is a square, each (α + uβ)-constacyclic code of length 4ps is expressed as a direct sum of two constacyclic codes of length 2ps. In the main case that the unit (α + uβ) is not a square, it is shown that the ambient ring (pm+upm)[x] (x4ps-(α+uβ)) is a principal ideal ring. From that, the structure, number of codewords, duals of all such (α + uβ)-constacyclic codes are obtained. As an application, we identify all self-orthogonal, dual-containing, and the unique self-dual (α + uβ)-constacyclic codes of length 4ps over pm + upm. |
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