Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 39 No. 1 (2021): Revista integración, temas de matemáticas
Research and Innovation Articles

Gray images of constacyclic codes over Galois rings R of nilpotency index 3.

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  • Angel R. García Ramírez,
  • Carlos A. López Andrade,
  • David Villa Hernández
Angel R. García Ramírez
BUAP
Carlos A. López Andrade
BUAP
David Villa Hernández
BUAP
DOI: https://doi.org/10.18273/revint.v39n1-2021005

Published 2021-05-19

How to Cite

García Ramírez, A. R., López Andrade, C. A., & Villa Hernández, D. (2021). Gray images of constacyclic codes over Galois rings R of nilpotency index 3. Revista Integración, Temas De matemáticas, 39(1), 57–78. https://doi.org/10.18273/revint.v39n1-2021005

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Abstract

We will state necessary and sufficient conditions for the image under the Gray map of a R-constacyclic code to be Fpm-quasi-cyclic code. We study the Witt vectors to get a way to operate the µ-reduction of padic components of the elements of the Galois rings of nilpotency index 3, R = GR(p3, m). We analyze Galois rings, its mostly relevant properties, and we focus in the p-adic representation of their elements. Later on, we examine construction of the Witt vectors rings and its operations, in particular, we get explicit expressions for operations of addition and product of the elements in the truncated Witt vectors ring of length 3, W3(Fpm). Finally, we will use these operations and an isomorphism between GR(p3, m) and W3(Fpm) to get a way to operate the µ-reductions described above.

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