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Linear codes with few weights over $\mathbb{F}_{p}+u\mathbb{F}_{p}$

Year: 2024

Type: preprint

Abstract: For any positive integer $m$ and an odd prime $p$; let $\mathbb{F}_{q}+u\mathbb{F}_{q}$, where $q=p^{m}$, be a ring extension of the ring $\mathbb{F}_{p}+u\mathbb{F}_{p}.$ In this paper, we construct linear codes over $\mathbb{F}_{p}+u\mathbb{F}_{p}$ by using trace function defined on $\mathbb{F}_{q}+u\mathbb{F}_{q}$ and determine their Hamming weight distributions by employing symplectic-weight distributions of their Gray images.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2406.18325

Authors: Kumar, Pavan, Khan, Noor Mohammad

Institutions: Aligarh Muslim University, Indian Institute of Science Bangalore

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: University Grants Commission, Aligarh Muslim University

Award: G4887626851

OpenAlex ID: W4400104794

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