Title :
On binary linear codes supporting t-designs
Author :
Lalaude-Labayle, Marc
Author_Institution :
Bordeaux I Univ., Talence, France
fDate :
9/1/2001 12:00:00 AM
Abstract :
In this paper, we present classification results on self-orthogonal binary codes supporting designs, Therefore, we use special linear forms on the intersection numbers. In particular, one shows that a binary self-orthogonal code of distance d⩽18 whose set of minimal-weight codewords supports a 5-design has to be self-dual. We also prove that the codewords of any fixed weight in a [24m+22, 12m+11, 4m+6] Type I code support a 3-design
Keywords :
binary codes; linear codes; 3-design; 5-design; Type I code; binary linear codes; binary self-orthogonal code; classification results; intersection numbers; linear forms; minimal-weight codewords; self-orthogonal binary codes; t-designs; Binary codes; Code standards; Cryptography; Hamming weight; Lattices; Linear code; Vectors;
Journal_Title :
Information Theory, IEEE Transactions on
