Explicit representation and enumeration of repeated-root (δ + αu<sup>2</sup>)-Constacyclic Codes over F<inf>2</inf><sup>m</sup>[u]/⟨u<sup>2?</sup>⟩
© 2013 IEEE. Let F2m be a finite field of 2m elements, λ and k be integers satisfying λ,k ≥ 2 and denote R= F2m[u]/‹ u2λ ›. Let δ,α F2m×. For any odd positive integer n, we give an explicit representation and enumeration for all distinct (δ +α u2)-constacyclic codes over R of l...
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| Main Authors: | , , , , |
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| Format: | Journal |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85082832767&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/70464 |
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| Institution: | Chiang Mai University |
| Summary: | © 2013 IEEE. Let F2m be a finite field of 2m elements, λ and k be integers satisfying λ,k ≥ 2 and denote R= F2m[u]/‹ u2λ ›. Let δ,α F2m×. For any odd positive integer n, we give an explicit representation and enumeration for all distinct (δ +α u2)-constacyclic codes over R of length 2kn, and provide a clear formula to count the number of all these codes. In particular, we conclude that every (δ +α u2)-constacyclic code over R of length 2kn is an ideal generated by at most 2 polynomials in the ring R[x]/‹ x2kn-(δ +α u2)›. As an example, we listed all 135 distinct (1+u2)-constacyclic codes of length 4 over F2[u]/‹ u4›, and apply our results to determine all 11 self-dual codes among them. |
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