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The preparata codes and a class of 4-designs

✍ Scribed by Alphonse H. Baartmans; Iliya Bluskov; Vladimir D. Tonchev

Publisher: John Wiley and Sons
Year: 1994
Tongue: English
Weight: 181 KB
Volume: 2
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.3180020307

No coin nor oath required. For personal study only.

✦ Synopsis

An extension theorem for t-designs is proved. As an application, a class of 4-(4" + 1,5,2) designs is constructed by extending designs related to the 3-designs formed by the minimum weight vectors in the Preparata code of length n = 4", m 2 2. 0 1994 John Wiley & Sons, Inc.

1 . INTRODUCTION

We assume familiarity with some basic notions from design theory and coding theory ) design D = (X, B) is a collection B of (not necessarily distinct) k-subsets (called blocks) of a v-set X (with elements called points) such that every t-subset of X is contained in precisely h blocks. A design with h = 1 is called a Steiner system, and the notation S(t, k , v) is often used in this case. Any t -(v, k , A) design is also an s-design for s 5 t with parameters s-(v, k , As), where (Cf.7 e.g.9 PI, [41, t71).

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