Ternary linear codes and quadrics.
The check positions of Hamming codes and the construction of a 2EC-AUED code.
The four known biplanes with k=11.
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 structure of generalized quasi cyclic codes.
Thetanullwerte and stable modular forms for Hecke groups.