Bibliographic Details
| Title: |
Constructions of Covering Sequences and Arrays |
| Authors: |
Chee, Yeow Meng, Etzion, Tuvi, Ta, Hoang, Vu, Van Khu |
| Publication Year: |
2025 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Combinatorics |
| More Details: |
An $(n,R)$-covering sequence is a cyclic sequence whose consecutive $n$-tuples form a code of length $n$ and covering radius $R$. Using several construction methods improvements of the upper bounds on the length of such sequences for $n \leq 20$ and $1 \leq R \leq 3$, are obtained. The definition is generalized in two directions. An $(n,m,R)$-covering sequence code is a set of cyclic sequences of length $m$ whose consecutive $n$-tuples form a code of length~$n$ and covering radius $R$. The definition is also generalized to arrays in which the $m \times n$ sub-matrices form a covering code with covering radius $R$. We prove that asymptotically there are covering sequences that attain the sphere-covering bound up to a constant factor. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2502.08424 |
| Accession Number: |
edsarx.2502.08424 |
| Database: |
arXiv |
