Some Applications of Magma in Designs and Codes: Oval Designs, Hermitian Unitals and Generalized Reed-Muller Codes

摘要

We describe three applications of Magma to problems in the area of designs and the associated codews: 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 Agd(Fp), where p is a prime.