论文信息 - On Composition of Four-Symbol δ-Codes and Hadamard Matrices

On Composition of Four-Symbol δ-Codes and Hadamard Matrices

It is shown that key instruments for composition of four-symbol 6-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 3-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.

C. H. Yang

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