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- W4386072004 abstract "Let R be an arbitrary finite commutative chain ring, γ be a fixed generator of the maximal ideal of R, and F <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>q</inf> = R/〈γ〉. In this paper, using the Generalized Discrete Fourier Transform, we derive the generator matrix of repeated-root quasi-cyclic codes of length n = ℓm, where q = 2 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>t</sup> , m = 2m <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>'</sup> , (m <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>'</sup> , 2) = 1 and $or{d_{m'}}left( {{2^t}} right) = m' - 1$, over R. Then, we specialize this result to derive the generator matrix for simple-root quasi-cyclic codes of length n = ℓm where ord <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</inf> (q) = m − 1. Our work presented in this paper can be used to find all classes of quasi-cyclic codes whose co-index satisfies these conditions. Finally, this method is used to list some binary quasi-cyclic codes with index 2 and find optimal and self-dual codes among them." @default.
- W4386072004 created "2023-08-23" @default.
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- W4386072004 date "2023-06-25" @default.
- W4386072004 modified "2023-09-27" @default.
- W4386072004 title "A Novel Construction Technique for Some Classes of Quasi-Cyclic Codes" @default.
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- W4386072004 doi "https://doi.org/10.1109/isit54713.2023.10206961" @default.
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