It is a well known fact that if C is an [n, k, d] formally self-dual even code with n > 30, then d ≤ 2[n/8]. A formally self-dual even code with d = 2[n/8] is called nearextremal. Kim and Pless [9] conjecture that there does not exist a near-extremal formally self dual even (not Type II) code of length n ≥ 48 with 8|n. In this paper, we prove that if n ≥ 72 and 8|n, then there is no near-extrem...

A detailed discussion of the point in polygon problem for arbitrary polygons is given. Two concepts for solving this problem are known in literature: the even-odd rule and the winding number, the former leading to ray-crossing, the latter to angle summation algorithms. First we show by mathematical means that both concepts are very closely related, thereby developing a first version of an algor...

Let C be a binary linear self-dual doubly-even code of length n and minimal weight d. Such codes exist only if 12 = 0 (mod 8). We put II = 24r + 8s, s = 0, 1, 2. It follows from the work of Gleason [2] and of Mallows and Sloane [6] that d s 4r + 4. C is called extremal if d = 4r + 4. In the following, an extremal code means a binary linear self-dual doubly-even extremal code. We use the set-the...