| Autor: |
Lijun Ma, Shuxia Liu, Zihong Tian |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 9, Iss 10, Pp 29333-29345 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.20241421?viewType=HTML |
| Popis: |
Quadrics are important in finite geometry and can be used to construct binary codes. In this paper, we first define an incidence matrix $ M $ based on points and non-degenerate quadrics in the classical projective space PG$ (n-1, q) $, where $ q $ is a prime power. As a consequence, we establish a binary code $ C(M) $ with the generator matrix $ M $ and determine the dimension of $ C(M) $ when $ q $ and $ n $ are both odd. In particular, we study the minimum distances of $ C(M) $ and $ C^{\perp}(M) $ in PG$ (2, q) $ and give their upper bounds. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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