✦ LIBER ✦
Some Applications of Magma in Designs and Codes: Oval Designs, Hermitian Unitals and Generalized Reed–Muller Codes
✍ Scribed by J.D. Key
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 286 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0747-7171
No coin nor oath required. For personal study only.
✦ Synopsis
We describe three applications of Magma to problems in the area of designs and the associated codes:
• Steiner systems, Hadamard designs and symmetric designs arising from an oval in an even-order plane, leading in the classical case to bent functions and difference-set designs; • the Hermitian unital as a 2-(q 3 + 1, q + 1, 1) design, and the code over Fp where p divides q + 1; • a basis of minimum-weight vectors for the code over Fp of the design of points and hyperplanes of the affine geometry AG d (Fp), where p is a prime.