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

Hai Q. Dinh, Bhanu Pratap Yadav, Bac T. Nguyen, Ashish Kumar Upadhyay, Woraphon Yamaka

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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.

Original languageEnglish
Pages (from-to)92898-92912
Number of pages15
JournalIEEE Access
Volume11
Early online date2023
DOIs
Publication statusPublished - 2023
MoE publication typeA1 Journal article-refereed

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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