Abstract
We give the parameters of any evaluation code on a smooth quadric surface. For hyperbolic quadrics the approach uses elementary results on product codes and the parameters of codes on elliptic quadrics are obtained by detecting a BCH structure on these codes and using the BCH bound. The elliptic quadric is a twist of the surface P 1 × P 1 and we detect a similar BCH structure on twists of the Segre embedding of a product of any d copies of the projective line.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 291-303 |
| Number of pages | 13 |
| Journal | Designs, Codes, and Cryptography |
| Volume | 66 |
| Issue number | 1-3 |
| DOIs | |
| State | Published - Jan 2013 |
Keywords
- Algebraic geometry codes
- BCH codes
- Evaluation codes
- Quadric surfaces
- Segre embedding
ASJC Scopus subject areas
- Computer Science Applications
- Applied Mathematics