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

Saroj Rani ()
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Saroj Rani: S. A. Jain P. G. College

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 2, 355-371

Abstract: 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.

Keywords: Negacyclic codes; Cyclic codes; Semi-local rings; 94B15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00001-2

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