Ternary constant weight codes.
Ternary linear codes and quadrics.
The (16,6,2) designs.
The check positions of Hamming codes and the construction of a 2EC-AUED code.
The four known biplanes with k=11.
The Gauss code problem off the plane.
The Hasse zeta function of a K3 surface related to the number of words of weight 5 in the Melas codes.
The Logogryph of Euler.
The Mathieu group and its pseudogroup extension .
The Nonexistence of [132, 6, 86]3 Codes and [135, 6, 88]3 Codes
We prove the nonexistence of [g3(6, d), 6, d]3 codes for d = 86, 87, 88, where g3(k, d) = ∑⌈d/3i⌉ and i=0 ... k−1. This determines n3(6, d) for d = 86, 87, 88, where nq(k, d) is the minimum length n for which an [n, k, d]q code exists.
The Nonexistence of some Griesmer Arcs in PG(4, 5)
In this paper, we prove the nonexistence of arcs with parameters (232, 48) and (233, 48) in PG(4,5). This rules out the existence of linear codes with parameters [232,5,184] and [233,5,185] over the field with five elements and improves two instances in the recent tables by Maruta, Shinohara and Kikui of optimal codes of dimension 5 over F5.
The number of inequivalent optimal covering codes.
The Number of Non-Isomorphic Hamiltonian Circuits in an -Dimensional Cube
The structure of generalized quasi cyclic codes.
The weight distribution of the functional codes defined by forms of degree 2 on Hermitian surfaces
We study the functional codes defined on a projective algebraic variety , in the case where is a non-degenerate Hermitian surface. We first give some bounds for , which are better than the ones known. We compute the number of codewords reaching the second weight. We also estimate the third weight, show the geometrical structure of the codewords reaching this third weight and compute their number. The paper ends with a conjecture on the fourth weight and the fifth weight of the code .
Thetanullwerte and stable modular forms for Hecke groups.
Trace and families of algebraic curves.
Transition restricted Gray codes.