Self-dual double circulant, self-dual double negacirculant and LCD double negacirculant codes over the ring F[]/⟨2-, 2-, ⟩

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date

2023

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Department of Information and Communications Engineering

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Mcode

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en

Pages

15

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IEEE Access, Volume 11, pp. 92898-92912

Abstract

In this paper, we investigate self-dual double circulant, and self-dual and linear complementary dual (LCD) double negacirculant codes over a finite ring R = F_q + u F_q + v F_q + uv F_q , where u^2=u , v^2=v , uv=vu and q=p^m. We study the algebraic structure of double circulant codes over R. We provide necessary and sufficient conditions for a double circulant code to be a self-dual code. We give a formula to get the total number of self-dual double circulant codes over the ring R. We compute distance bounds for self-dual double circulant codes over R. In addition, by using a Gray map, we show that the families of self-dual double circulant codes under the Gray map are asymptotically good. Moreover, the algebraic structure of double negacirculant codes and necessary and sufficient conditions for a double negacirculant code to be a self-dual code and to be an LCD code are also given. We determine the total number of self-dual and LCD double negacirculant codes over R.

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Keywords

Artin conjecture, Codes, Double circulant codes, double negacirculant codes, Dual band, Finite element analysis, Gray map, Hamming weight, LCD codes, Linear codes, Liquid crystal displays, Object recognition, self-dual codes, Structural rings

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DOI

10.1109/ACCESS.2023.3309246

Citation

Dinh, H Q, Yadav, B P, Nguyen, B T, Upadhyay, A K & Yamaka, W 2023, 'Self-dual double circulant, self-dual double negacirculant and LCD double negacirculant codes over the ring F[]/⟨2-, 2-, ⟩', IEEE Access, vol. 11, pp. 92898-92912. https://doi.org/10.1109/ACCESS.2023.3309246

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https://urn.fi/URN:NBN:fi:aalto-202309135813

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