Minimum distance decoding of general algebraic geometry codes via lists
IEEE Transactions on Information Theory
| Hi-index | 754.90 |
In IEEE Transactions on Information Theory , vol. 48, no. 2, pp. 535-537, Feb. 2002, Xing and Chen show that there exist algebraic-geometry (AG) codes from the Hermitian function field over Fq2 constructed using Fq2-rational divisors which are improvements over the much-studied one-point Hermitian codes. In this correspondence, we construct such codes by using a place P of degree r 1. This motivates a study of gap numbers and pole numbers at places of higher degree. In fact, the code parameters are estimated using the Weierstrass gap set of the place P and relating it to the gap set of the r-tuple of places of degree one lying over P in a constant field extension of degree r.