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Computer Science > Information Theory

arXiv:2201.07113 (cs)
[Submitted on 18 Jan 2022]

Title:Three Weight Ternary Linear Codes from Non-Weakly Regular Bent Functions

Authors:Rumi Melih Pelen
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Abstract:In this paper, several classes of three-weight ternary linear codes from non-weakly regular dual-bent functions are constructed based on a generic construction method. Instead of the whole space, we use the subspaces $B_+(f)$ or $B_-(f)$ associated with a ternary non-weakly regular dual-bent function $f$. Unusually, we use the pre-image sets of the dual function $f^*$ in $B_+(f)$ or $B_-(f)$ as the defining sets of the corresponding codes. Since the size of the defining sets of the constructed codes is flexible, it enables us to construct several codes with different parameters for a fixed dimension. We represent the weight distribution of the constructed codes. We also give several examples.
Comments: 22 pages
Subjects: Information Theory (cs.IT); Combinatorics (math.CO)
MSC classes: 94A05, 94A11, 94B05 (Primary), 94A24, 94A62 (Secondary)
Cite as: arXiv:2201.07113 [cs.IT]
  (or arXiv:2201.07113v1 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2201.07113

Submission history

From: Rumi Melih Pelen [view email]
[v1] Tue, 18 Jan 2022 16:42:05 UTC (21 KB)
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