English Abstract
Abstract:
In this paper we consider the Hermitian curve yq0 + y = xq0+1 over the feld 픽q(q ∶= q2 0). The automorphism group of this curve is known to be the projective unitary group PGU(3, q) = 2A2(q) with q3
0(q3 0 + 1)(q2 0 − 1) elements. We follow the construction done for the Suzuki code in Eid et al. (Designs Codes Cryptogr 81(3):413–425, 2016, https://doi.org/10.1007/s10623-015-0164-5). We construct
algebraic geometry codes over 픽q3 from an 2A2(q)-invariant divisor D, give an explicit basis for the Riemann–Roch space L(퓁D) for 0 < 퓁 ≤ q3 0 − 1. These families of codes have good parameters and information rate close to one. In addition, they are explicitly constructed. The dual codes of these families are of the same kind if q3 0 − 2g + 1 ≤ 퓁 ≤ q3 0 − 1.
