On constacyclic codes of length <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mn>4</mml:mn><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msup></mml:math> over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml2" display="inline" overflow="scroll" altimg="si2.gif"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">F</mml:mi></mml:mrow><mml:mrow><mml:msup><mml:mrow>

Dinh, Hai Q.; Dhompongsa, Sompong; Sriboonchitta, Songsak

doi:10.1016/j.disc.2016.11.014

Cited by 47 publications

(55 citation statements)

References 28 publications

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“…For any odd prime p such that p m ≡ 1 (mod 4), (α + uβ)-constacyclic codes of length 4p s over R are provided in [31].…”

Section: Introductionmentioning

confidence: 99%

“…(x 4 −η 3 ) p s , respectively. The classification, detailed structure, and number of codewords of constacyclic codes C of length 4p s over R are completely determined in [31]. Hence, the classification, detailed structure, and number of codewords of negacyclic codes C of length 8p s over R can be obtained from that of the direct summands C 1 and C 2 .…”

Section: Introductionmentioning

confidence: 99%

“…By [31,Proposition 5.4], we have T = min{i, p s − i + t}. Then we can see that the ideals to be distinct if i + j < T .…”

Section: Introductionmentioning

confidence: 99%

“…• Case 4b: If h(x) is a unit, using [31,Proposition 5.5], then T = min{i, p s − i + t}, and h(x) can be expressed as…”

Section: Introductionmentioning

confidence: 99%

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Constacyclic codes of length $ 8p^s $ over $ \mathbb F_{p^m} + u\mathbb F_{p^m} $

Dinh

Nguyen

Maneejuk

2022

AMC

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<p style='text-indent:20px;'>For any odd prime <inline-formula><tex-math id="M3">\begin{document}$ p $\end{document}</tex-math></inline-formula>, the structures and duals of <inline-formula><tex-math id="M4">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>-constacyclic codes of length <inline-formula><tex-math id="M5">\begin{document}$ 8p^s $\end{document}</tex-math></inline-formula> over <inline-formula><tex-math id="M6">\begin{document}$ \mathcal R = \mathbb F_{p^m}+u\mathbb F_{p^m} $\end{document}</tex-math></inline-formula> are completely determined for all unit <inline-formula><tex-math id="M7">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula> of the form <inline-formula><tex-math id="M8">\begin{document}$ \lambda = \xi^l\in \mathbb F_{p^m} $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M9">\begin{document}$ l $\end{document}</tex-math></inline-formula> is even. In addition, the algebraic structures of all cyclic and negacyclic codes of length <inline-formula><tex-math id="M10">\begin{document}$ 8p^s $\end{document}</tex-math></inline-formula> over <inline-formula><tex-math id="M11">\begin{document}$ \mathcal R $\end{document}</tex-math></inline-formula> are established in term of their generator polynomials. Dual codes of all cyclic and negacyclic codes of length <inline-formula><tex-math id="M12">\begin{document}$ 8p^s $\end{document}</tex-math></inline-formula> over <inline-formula><tex-math id="M13">\begin{document}$ \mathcal R $\end{document}</tex-math></inline-formula> are also investigated. Furthermore, we give the number of codewords in each of those cyclic and negacyclic codes. We also obtain the number of cyclic and negacyclic codes of length <inline-formula><tex-math id="M14">\begin{document}$ 8p^s $\end{document}</tex-math></inline-formula> over <inline-formula><tex-math id="M15">\begin{document}$ \mathcal R $\end{document}</tex-math></inline-formula>.</p>

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“…For any odd prime p such that p m ≡ 1 (mod 4), (α + uβ)-constacyclic codes of length 4p s over R are provided in [31].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Constacyclic codes of length $ 8p^s $ over $ \mathbb F_{p^m} + u\mathbb F_{p^m} $

Dinh

Nguyen

Maneejuk

2022

AMC

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“…Chen et al [7] investigated constacyclic codes of length 2p s over F p m + uF p m . Recently, Dinh et al [11] [12] studied constacyclic codes of length 4p s over F p m + uF p m . These papers mainly used the methods in [8] and [9], and the main results and their proofs depend heavily on the code lengths p s , 2p s and 4p s .…”

Section: Introductionmentioning

confidence: 99%

Constacyclic codes of length <inline-formula><tex-math id="M1">\begin{document}$np^s$\end{document}</tex-math></inline-formula> over <inline-formula><tex-math id="M2">\begin{document}$\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$\end{document}</tex-math></inline-formula>

Cao¹,

Chen²,

Dinh³

et al. 2018

Advances in Mathematics of Communications

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Let F p m be a finite field of cardinality p m and R = F p m [u]/ u 2 = F p m + uF p m (u 2 = 0), where p is a prime and m is a positive integer. For any λ ∈ F × p m , an explicit representation for all distinct λ-constacyclic codes over R of length np s is given by a canonical form decomposition for each code, where s and n are arbitrary positive integers satisfying gcd(p, n) = 1. For any such code, using its canonical form decomposition the representation for the dual code of the code is provided. Moreover, representations for all distinct cyclic codes, negacyclic codes and their dual codes of length np s over R are obtained, and self-duality for these codes are determined. Finally, all distinct self-dual negacyclic codes over F 5 + uF 5 of length 2 • 3 t • 5 s are listed for any positive integer t.

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Quantum MDS and synchronizable codes from cyclic codes of length $$5p^s$$ over $$\mathbb F_{p^m}$$

Dinh

Nguyen

Tansuchat

2021

AAECC

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On constacyclic codes of length 4ps over F

Cited by 47 publications

References 28 publications

Constacyclic codes of length $ 8p^s $ over $ \mathbb F_{p^m} + u\mathbb F_{p^m} $

Constacyclic codes of length $ 8p^s $ over $ \mathbb F_{p^m} + u\mathbb F_{p^m} $

Constacyclic codes of length <inline-formula><tex-math id="M1">\begin{document}$np^s$\end{document}</tex-math></inline-formula> over <inline-formula><tex-math id="M2">\begin{document}$\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$\end{document}</tex-math></inline-formula>

Quantum MDS and synchronizable codes from cyclic codes of length $$5p^s$$ over $$\mathbb F_{p^m}$$

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