Self-orthogonal designs and extremal doubly even codes

On self-dual doubly-even extremal codes

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...

Mutually disjoint t-designs and t-SEEDs from extremal doubly-even self-dual codes

It is known that extremal doubly-even self-dual codes of length n ≡ 8 or 0 (mod 24) yield 3or 5-designs respectively. In this paper, by using the generator matrices of bordered double circulant doubly-even self-dual codes, we give 3-(n, k; m)-SEEDs with (n, k, m) ∈ {(32, 8, 5), (56, 12, 9), (56, 16, 9), (56, 24, 9), (80, 16, 52)}. With the aid of computer, we obtain 22 generator matrices of bor...

On the support designs of extremal binary doubly even self-dual codes

Several errors in the original publication of this article are noted. It has been corrected in this erratum. Theorem 4.2 In the proof of Theorem 4.2, the computation of F(63,4·63+4;[0,2,4,6,8,10,12,14]) 10321920 is incorrect. We exchange “Let D′′ be a self-orthogonal . . . (page 535, line 5 up)” to Let D′′ be a self-orthogonal 8-(24m, 4m + 4, λ8) design, where λ8 = (5m−2 m−1 ) (4m−1)(4m−2)(4m−3...

The mass of extremal doubly-even self-dual codes of length 40

We determine the mass of extremal doubly-even self-dual binary codes of length 40. It follows that there are at least 12579 such codes. keywords: extremal Type II codes, unimodular lattices

Orthogonal designs and MDS self-dual codes