Kloosterman sums over finite Frobenius rings

On Kloosterman sums over finite fields of characteristic 3

We study the divisibility by 3 of Kloosterman sums K(a) over finite fields of characteristic 3. We give a simple recurrent algorithm for finding the largest k, such that 3 divides the Kloosterman sum K(a). This gives a simple description of zeros of such Kloosterman sums.

Gauss Sums and Kloosterman Sums over Residue Rings of Algebraic Integers

Let O denote the ring of integers of an algebraic number field of degree m which is totally and tamely ramified at the prime p. Write ζq = exp(2πi/q), where q = pr. We evaluate the twisted Kloosterman sum ∑ α∈(O/qO)∗ χ(N(α))ζ T (α)+z/N(α) q , where T and N denote trace and norm, and where χ is a Dirichlet character (mod q). This extends results of Salié for m = 1 and of Yangbo Ye for prime m di...

Witt Theorems for Linear Codes over Finite Frobenius Rings

Matrix product codes over finite commutative Frobenius rings

Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes constructed with several types of matrices is bounded in different ways. The duals of matrix product codes are also explicitly described in terms of matrix product codes.

On Plotkin-Optimal Codes over Finite Frobenius Rings

We study the Plotkin bound for codes over a finite Frobenius ring R equipped with the homogeneous weight. We show that for codes meeting the Plotkin bound, the distribution on R induced by projection onto a coordinate has an interesting property. We present several constructions of codes meeting the Plotkin bound and of Plotkin-optimal codes. We also investigate the relationship between Butson-...