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On Composition of Four-Symbol δ-Codes and Hadamard Matrices
C. H. Yang
Proceedings of the American Mathematical Society
Vol. 107, No. 3 (Nov., 1989), pp. 763-776
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2048177
Page Count: 14
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It is shown that key instruments for composition of four-symbol δ-codes are the Lagrange identity for polynomials, a certain type of quasi-symmetric 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 δ-codes of length (2n + 1)t (or nt) 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 = (2n + 1)t (or nt). Other related topics are also discussed.
Proceedings of the American Mathematical Society © 1989 American Mathematical Society