Hasse-Davenport Curves, Gauss Sums, and Weight Distributions of Irreducible Cyclic Codes

Calculs de Certaines Sommes de Gauss

“…Dans cet article, nous re solvons le probleÁ me des sommes de Gauss dans une situation analogue en supposant que m est une puissance d'un nombre premier. Lorsque m est produit de deux nombres premiers, voir [14].…”

Quadratic Gauss Sums

“…An interesting situation is the index 2 case, i.e., that in which the subgroup 1p2, generated by p, has index 2 in (9/m9)*. In [9], this case was studied under the assumption that p"2 and m is a product of two distinct primes. In this index 2 case the Gauss sums have been calculated if m"l in [1], and if m"lP in [7], where l is a prime such that l'3, l,3 (mod 4).…”

Sums of Gauss sums and weights of irreducible codes

“…They have only been computed when the subgroup generated by 2 in (Z/dZ) * has index 2 or contains −1, see [1,6,11,15]. For applications of these computations to irreducible codes see [1][2][3]12,14].…”