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Constructions of Goethals–Seidel Sequences by Using k -Partition

Author

Listed:
  • Shuhui Shen

    (School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Xiaojun Zhang

    (School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China)

Abstract

In this paper, we are devoted to finding Goethals–Seidel sequences by using k -partition, and based on the finite Parseval relation, the construction of Goethals–Seidel sequences could be transformed to the construction of the associated polynomials. Three different structures of Goethals–Seidel sequences will be presented. We first propose a method based on T-matrices directly to obtain a quad of Goethals–Seidel sequences. Next, by introducing the k -partition, we utilize two classes of 8-partitions to obtain a new class of polynomials still remaining the same (anti)symmetrical properties, with which a quad of Goethals–Seidel sequences could be constructed. Moreover, an adoption of the 4-partition together with a quad of four symmetrical sequences can also lead to a quad of Goethals–Seidel sequences.

Suggested Citation

  • Shuhui Shen & Xiaojun Zhang, 2023. "Constructions of Goethals–Seidel Sequences by Using k -Partition," Mathematics, MDPI, vol. 11(2), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:294-:d:1026824
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    References listed on IDEAS

    as
    1. Víctor Álvarez & José Andrés Armario & María Dolores Frau & Félix Gudiel & María Belén Güemes & Amparo Osuna, 2021. "Hadamard Matrices with Cocyclic Core," Mathematics, MDPI, vol. 9(8), pages 1-14, April.
    2. José Andrés Armario, 2021. "Boolean Functions and Permanents of Sylvester Hadamard Matrices," Mathematics, MDPI, vol. 9(2), pages 1-8, January.
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    Cited by:

    1. Shuhui Shen & Xiaojun Zhang, 2024. "Several Goethals–Seidel Sequences with Special Structures," Mathematics, MDPI, vol. 12(4), pages 1-13, February.

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