Bibliographic Details
| Title: |
Maximum Size $t$-Intersecting Families and Anticodes |
| Authors: |
Wang, Xuan, Etzion, Tuvi, Krotov, Denis, Shi, Minjia |
| Publication Year: |
2025 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Combinatorics |
| More Details: |
The maximum size of $t$-intersecting families is one of the most celebrated topics in combinatorics, and its size is known as the Erd\H{o}s-Ko-Rado theorem. Such intersecting families, also known as constant-weight anticodes in coding theory, were considered in a generalization of the well-known sphere-packing bound. In this work we consider the maximum size of $t$-intersecting families and their associated maximum size constant-weight anticodes over alphabet of size $q >2$. It is proved that the structure of the maximum size constant-weight anticodes with the same length, weight, and diameter, depends on the alphabet size. This structure implies some hierarchy of constant-weight anticodes. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2503.15116 |
| Accession Number: |
edsarx.2503.15116 |
| Database: |
arXiv |
