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PreprintCC BY-NC-ND 4.0arXiv

Linear Codes over 𝔽q+u𝔽q associated with Simplicial Complexes, Their Gray Images, and Subfield Codes

  • Ankit Yadav
  • Akanksha Tiwari
  • Ritumoni Sarma
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Abstract

In recent years, simplicial complexes have gained considerable attention as a useful tool for constructing distance-optimal codes over finite fields. In this article, we construct four infinite families of linear codes over the ring β„›=𝔽q+u𝔽q with u2=0 using simplicial complexes with one or two maximal elements, and completely determine their Lee weight distributions via exponential-sum techniques. By employing a Gray map on β„›, we obtain infinite families of distance-optimal codes over 𝔽q, including a near-Griesmer family, and establish sufficient conditions for their minimality. Furthermore, we investigate the corresponding subfield codes and derive sufficient conditions for their distance-optimality and minimality, yielding infinite families of Griesmer and near-Griesmer codes.

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Cite

BibTeXRIS
BibTeX
@misc{yadav2026linear,
  title = {{Linear Codes over $\mathbbF_q+u\mathbbF_q$ associated with Simplicial Complexes, Their Gray Images, and Subfield Codes}},
  author = {Ankit Yadav and Akanksha Tiwari and Ritumoni Sarma},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11783},
  eprint = {2609.11783},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11783},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Linear Codes over 𝔽_q+u𝔽_q associated with Simplicial Complexes, Their Gray Images, and Subfield Codes
AU  - Ankit Yadav
AU  - Akanksha Tiwari
AU  - Ritumoni Sarma
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11783
UR  - https://arxiv.org/abs/2609.11783
AB  - In recent years, simplicial complexes have gained considerable attention as a useful tool for constructing distance-optimal codes over finite fields. In this article, we construct four infinite families of linear codes over the ring β„›=𝔽_q+u𝔽_q with u^2=0 using simplicial complexes with one or two maximal elements, and completely determine their Lee weight distributions via exponential-sum techniques. By employing a Gray map on β„›, we obtain infinite families of distance-optimal codes over 𝔽_q, including a near-Griesmer family, and establish sufficient conditions for their minimality. Furthermore, we investigate the corresponding subfield codes and derive sufficient conditions for their distance-optimality and minimality, yielding infinite families of Griesmer and near-Griesmer codes.
ER  -