Constructions of Goethals–Seidel Sequences by Using k -Partition

Shuhui Shen and Xiaojun Zhang ()
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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

Mathematics, 2023, vol. 11, issue 2, 1-12

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.

Keywords: symmetry and antisymmetry; Goethals–Seidel sequences; T-matrices; k -partition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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