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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A composition theorem for $ \delta $-codes


Author: C. H. Yang
Journal: Proc. Amer. Math. Soc. 89 (1983), 375-378
MSC: Primary 94B60; Secondary 05A19, 05B20
MathSciNet review: 712655
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Abstract: If Golay complementary sequences (or equivalently a two-symbol $ \delta $-code) of length $ n$ and a Turyn $ \delta $-code of length $ t$ exist then four-symbol $ \delta $-codes of length $ (2n + 1)/t$ can be composed. Therefore new families of Hadamard matrices of orders $ 4uw$ and $ 20uw$ can be constructed, where $ u = ({2^{\alpha + 1}}{10^b}{26^c} + 1)t$ for odd $ t \leqslant 59$ or $ t = {2^d}{10^e}{26^f} + 1$ (all $ a$, $ b$, $ c$, $ d$, $ e$, and $ f \geqslant 0$), and $ w$ is the order of Williamson matrices.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0712655-2
PII: S 0002-9939(1983)0712655-2
Article copyright: © Copyright 1983 American Mathematical Society