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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On composition of four-symbol $ \delta$-codes and Hadamard matrices


Author: C. H. Yang
Journal: Proc. Amer. Math. Soc. 107 (1989), 763-776
MSC: Primary 94B60; Secondary 05B20, 62K10
MathSciNet review: 979054
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Abstract: It is shown that key instruments for composition of four-symbol $ \delta $-codes are the Lagrange identity for polynomials, a certain type of quasisymmetric sequences (i.e., a set of normal or near normal sequences) and base sequences. The following is proved: If a set of base sequences for length $ t$ and a set of normal (or near normal) sequences for length $ n$ exist then four-symbol $ \delta $-codes of length $ \left( {2n + 1} \right)t\left( {{\text{or }}nt} \right)$ can be composed by application of the Lagrange identity. Consequently a new infinite family of Hadamard matrices of order $ 4uw$ can be constructed, where $ w$ is the order of Williamson matrices and $ u = \left( {2n + 1} \right)t\left( {{\text{or }}nt} \right)$. Other related topics are also discussed.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0979054-5
Article copyright: © Copyright 1989 American Mathematical Society