A strengthening of the Assmus-Mattson theorem

An Assmus-Mattson theorem for Z4-codes

The Assmus{Mattson theorem is a method to nd designs in linear codes over a nite eld. The purpose of this paper is to give an analogue of this theorem for Z 4 -codes by using the harmonic weight enumerator which is introduced by Bachoc. This theorem can nd some 5-designs in the lifted Golay code over Z 4 which were discovered previously by other methods. Index Terms { Z 4 -codes, Assmus{Mattson...

New proofs of the Assmus-Mattson theorem based on the Terwilliger algebra

We use the Terwilliger algebra to provide a new approach to the Assmus-Mattson theorem. This approach also includes another proof of the minimum distance bound shown by Martin as well as its dual.

An Assmus-Mattson theorem for codes over commutative association schemes

A criterion for designs in Z 4 - codes on the symmetrized weight enumerator

The Assmus{Mattson theorem is a method to nd designs in linear codes over a nite eld. It is an interesting problem to nd an analogue of the theorem for Z 4 -codes. The author once gave a candidate of the theorem. The purpose of this paper is an improvement of the theorem. It is known that the lifted Golay code over Z 4 contains 5-designs on Lee compositions. The improved method can nd some of t...

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...