On a class of constacyclic codes of length 4ps over ð ½pm + uð ½pm
© 2019 World Scientific Publishing Company Let (Formula presented.) be a prime such that (Formula presented.) (mod 4). For any unit (Formula presented.) of (Formula presented.), we determine the algebraic structures of (Formula presented.)-constacyclic codes of length (Formula presented.) over the f...
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| Main Authors: | , , , |
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| Format: | Journal |
| Published: |
2018
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| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85044442291&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/48455 |
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| Institution: | Chiang Mai University |
| Summary: | © 2019 World Scientific Publishing Company Let (Formula presented.) be a prime such that (Formula presented.) (mod 4). For any unit (Formula presented.) of (Formula presented.), we determine the algebraic structures of (Formula presented.)-constacyclic codes of length (Formula presented.) over the finite commutative chain ring (Formula presented.), (Formula presented.). If the unit (Formula presented.) is a square, each (Formula presented.)-constacyclic code of length (Formula presented.) is expressed as a direct sum of an -(Formula presented.)-constacyclic code and an (Formula presented.)-constacyclic code of length (Formula presented.) If the unit (Formula presented.) is not a square, then (Formula presented.) can be decomposed into a product of two irreducible coprime quadratic polynomials which are (Formula presented.) and (Formula presented.), where (Formula presented.) and (Formula presented.). By showing that the quotient rings (Formula presented.) and (Formula presented.) are local, non-chain rings, we can compute the number of codewords in each of (Formula presented.)-constacyclic codes. Moreover, the duals of such codes are also given. |
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