Euclidean concomitants of the ternary cubic

The Euclidean Algorithm in Cubic Number Fields

In this note we present algorithms for computing Euclidean minima of cubic number fields; in particular, we were able to find all normEuclidean cubic number fields with discriminants −999 < d < 104.

Some ternary cubic two-weight codes

We study trace codes with defining set L, a subgroup of the multiplicative group of an extension of degree m of the alphabet ring F3+uF3+u 2 F3, with u 3 = 1. These codes are abelian, and their ternary images are quasi-cyclic of co-index three (a.k.a. cubic codes). Their Lee weight distributions are computed by using Gauss sums. These codes have three nonzero weights when m is singly-even and |...

Neurological concomitants of uveitis.

AIM To describe the prevalence and types of neurological disease that occur in association with uveitis. METHODS Retrospective review of medical records of patients attending a tertiary referral uveitis service over a 15 year period. RESULTS Of 1450 patients with uveitis, 115 (7.9%) had neurological disease that was considered to be causally related to the eye inflammation. The most frequen...

Non-Galois cubic fields which are Euclidean but not norm-Euclidean

Weinberger in 1973 has shown that under the Generalized Riemann Hypothesis for Dedekind zeta functions, an algebraic number field with infinite unit group is Euclidean if and only if it is a principal ideal domain. Using a method recently introduced by us, we give two examples of cubic fields which are Euclidean but not norm–Euclidean. Let R be the ring of integers of an algebraic number field ...

Biologic concomitants of alcoholism.