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Abstract: The normal sequences NSn and near-normal sequences NNn play an importantrole in the construction of orthogonal designs and Hadamard matrices. They canbe identified with certain base sequences A;B;C;D, where A and B have lengthn+1 and C and D length n. C.H. Yang conjectured that near-normal sequencesexist for all even n. While this has been confirmed for n not exceeding 30, sofar nothing else was known for larger n. We show that NN32 consists of 8equivalence classes and we exhibit their representatives. We also constructrepresentatives for two equivalence classes of NN34. On the other hand ourexhaustive computer searches show that NS31 and NS33 are void.



Author: Dragomir Z. Djokovic

Source: https://arxiv.org/







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