An Assmus-Mattson theorem for Z4-codes

An Assmus-Mattson theorem for codes over commutative association schemes

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.

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...

Codes of Small Defect

The parameters of a linear code C over GF(q) are given by [n, k, d], where n denotes the length, k the dimension and d the minimum distance of C . The code C is called MDS, or maximum distance separable, if the minimum distance d meets the Singleton bound, i.e. d = n−k+1. Unfortunately, the parameters of an MDS code are severely limited by the size of the field. Thus we look for codes which hav...

A strengthening of the Assmus-Mattson theorem

Let w 1 = d, w 2 , ... , w s be the weights of the nonzero codewords in a binary linear [n , k, d] code C, and let w1′ , w2′ , ... , ws ′ ′ be the nonzero weights in the dual code C ⊥ . Let t be an integer in the range 0 < t < d such that there are at most d − t weights wi′ with 0 < wi′ ≤ n − t. Assmus and Mattson proved that the words of any weight w i in C form a t-design. We show that if w 2...