On composition of four-symbol -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 -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 and a set of normal (or near normal) sequences for length exist then four-symbol -codes of length can be composed by application of the Lagrange identity. Consequently a new infinite family of Hadamard matrices of order can be constructed, where is the order of Williamson matrices and . 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