A coding theoretic approach to extending designs

✍ Scribed by George T. Kennedy; Vera Pless

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 1003 KB
• Volume: 142
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(94)00010-g

✦ Synopsis

We introduce the study of designs in a coset of a binary code which can be held by vectors of a fixed weight. If C is a binary [2n, n, d] code with n odd and the words of weights n -1 and n + 1 hold complementary t-designs, then we show that the vectors of weight n in a coset of weight 1 also hold a t-design. We also show how to "extend" these designs. We then consider designs in cosets of type I self-dual codes, in particular in the shadow. If the vectors of a fixed weight in the code hold t-designs then so do the vectors of a fixed weight in the shadow. For [24k -2,12k -1,2 + 4/c] type I codes, these designs extend to designs in the type II parent code.