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A class of constacyclic codes over $${\mathbb{F}}_{p^m}[u]/\left\langle u^2\right\rangle$$ F p m [ u ] / u 2

Author

Listed:
  • Saroj Rani

    (S. A. Jain P. G. College)

Abstract

Let p be an odd prime, and let m be a positive integer satisfying $$p^m \equiv 3~(\text {mod }4).$$ p m ≡ 3 ( mod 4 ) . Let $$\mathbb {F}_{p^m}$$ F p m be the finite field with $$p^m$$ p m elements, and let $$R=\mathbb {F}_{p^m}[u]/\left\langle u^2\right\rangle$$ R = F p m [ u ] / u 2 be the finite commutative chain ring with unity. In this paper, we determine all constacyclic codes of length $$4p^s$$ 4 p s over R and their dual codes, where s is a positive integer. We also determine their sizes and list some isodual constacyclic codes of length $$4p^s$$ 4 p s over R.

Suggested Citation

  • Saroj Rani, 2022. "A class of constacyclic codes over $${\mathbb{F}}_{p^m}[u]/\left\langle u^2\right\rangle$$ F p m [ u ] / u 2," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(2), pages 355-371, June.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:2:d:10.1007_s13226-021-00001-2
    DOI: 10.1007/s13226-021-00001-2
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