Many problems in coding theory are related to the problem of determining the distribution of the number of rational points in a family of algebraic curves defined over a finite field. Usually, these problems are very hard and a complete answer is often out of reach. In the present paper we consider the problem of the weight distributions of the cosets of certain BCH codes. This problem turns ou...

Investigating a conjecture of Zannier, we study irreducible subvarieties abelian schemes that dominate the base and contain Zariski dense set torsion points lie on pairwise isogenous fibers. If everything is defined over algebraic numbers scheme has maximal variation, prove geometric generic fiber such subvariety union cosets. We go to fully or partially explicit versions this result in fibered...

We determine all linear codes C containing the constant code E, for which there is a weight-preserving group of semilinear automorphisms which acts transitively on the set of nontrivial cosets of E in C.

From cosets of binary Hamming codes we construct diameter perfect constantweight ternary codes with weight n − 1 (where n is the code length) and distances 3 and 5. The class of distance 5 codes has parameters unknown before.