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Quasi-Symmetric Designs and Codes Meeting the Grey–Rankin Bound

✍ Scribed by Gary McGuire


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
261 KB
Volume
78
Category
Article
ISSN
0097-3165

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✦ Synopsis


We give a characterization of codes meeting the Grey Rankin bound. When the codes have even length, the existence of such codes is equivalent to the existence of certain quasi-symmetric designs. We also find the parameters of all linear codes meeting the Grey Rankin bound.

1997 Academic Press

Theorem A. Suppose n and d satisfy n&-n<2d<n. Then:

(i) If n is odd, there exists a self-complementary code meeting the Grey Rankin bound if and only if there exists a Hadamard matrix of size n+1.