Codebooks from generalized bent \(\mathbb{Z}_4\)-valued quadratic forms

DOI10.1016/J.DISC.2019.111736zbMath1487.94200arXiv1905.08834OpenAlexW2947214501MaRDI QIDQ2286597

Yanfeng Qi, Sihem Mesnager, Chun-Ming Tang

Publication date: 22 January 2020

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.08834

zbMATH Keywords

codebookquadratic formGalois ringgeneralized bent function

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Bounds on codes (94B65) Quadratic forms over local rings and fields (11E08) Boolean functions (94D10) Finite commutative rings (13M99)

Related Items (2)

Nearly optimal codebooks from generalized Boolean bent functions over \(\mathbb{Z}_4\) ⋮ Cayley sum graphs and their applications to codebooks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimal codebooks achieving the Levenshtein bound from generalized bent functions over \(\mathbb {Z}_{4}\)
• Steiner equiangular tight frames
• Generalized Gray map and a class of \(p\)-ary nonlinear codes
• Construction of cyclotomic codebooks nearly meeting the Welch bound
• Four decades of research on bent functions
• Codebooks from almost difference sets
• Grassmannian frames with applications to coding and communication
• Nearly optimal codebooks based on generalized Jacobi sums
• Two families of nearly optimal codebooks
• Gauss periods and codebooks from generalized cyclotomic sets of order four
• Generalizations of the Kervaire invariant
• Optimal Codebooks From Binary Codes Meeting the Levenshtein Bound
• New Families of Codebooks Achieving the Levenstein Bound
• New Constructions of Quadratic Bent Functions in Polynomial Form
• New families of binary sequences with low correlation
• Achieving the Welch Bound With Difference Sets
• Complex Codebooks From Combinatorial Designs
• A Generic Construction of Complex Codebooks Meeting the Welch Bound
• Lower bounds on the maximum cross correlation of signals (Corresp.)
• The Z/sub 4/-linearity of Kerdock, Preparata, Goethals, and related codes
• Z₄ -Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets
• Packing Lines, Planes, etc.: Packings in Grassmannian Spaces
• ${\BBZ}_4$-Valued Quadratic Forms and Quaternary Sequence Families
• New Optimal Quadriphase Sequences With Larger Linear Span
• Two Classes of Codebooks Nearly Meeting the Welch Bound
• Bent Functions
• An introduction to frames and Riesz bases

This page was built for publication: Codebooks from generalized bent \(\mathbb{Z}_4\)-valued quadratic forms