One-Point Codes Using Places of Higher Degree
Gretchen L. Matthews, Thierry Michel · IEEE Transactions on Information Theory · 2005
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 F/sub q//sup 2/ constructed using F/sub q//sup 2/-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.