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Spherical codes attached to complex weighing matrices
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DOI：10.1016/j.disc.2025.114860.png)
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Abstract
En 中文
We introduce the notion of a bent sequence attached to a weighing matrix. With every weighing matrix, we associate a spherical code in dimension twice the order of the matrix. Its covering and packing properties are studied, and under mild conditions, it is shown to be a spherical design of strength two. The bent sequences provide a lower bound, and the design property an upper bound on the covering radius of the code. Exact values are determined by using a geometric technique (Delaunay diagram). Computational methods based on Gr & ouml;bner bases and linear algebra are given to construct bent sequences. Balancedly splittable matrices provide constructions of weighing matrices with designed bent sequences. (c) 2025 Published by Elsevier B.V.
Keywords:
Weighing matrices
Spherical designs
Bent sequences
Spherical codes
Covering radius
Journal
D
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0.9
Papers:
285
Citations:
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