Optimal codebooks achieving the Levenshtein bound from generalized bent functions over \(\mathbb {Z}_{4}\)
From MaRDI portal
Publication:502403
DOI10.1007/S12095-016-0194-5zbMath1380.94154OpenAlexW2465189940MaRDI QIDQ502403
Publication date: 5 January 2017
Published in: Cryptography and Communications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s12095-016-0194-5
Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Bounds on codes (94B65) Boolean functions (94D10)
Related Items (10)
Nearly optimal codebooks from generalized Boolean bent functions over \(\mathbb{Z}_4\) ⋮ Constructions of asymptotically optimal codebooks with respect to Welch bound and Levenshtein bound ⋮ Hybrid character sums and near-optimal partial Hadamard codebooks ⋮ Character sums over a non-chain ring and their applications ⋮ Properties of tight frames that are regular schemes ⋮ Two constructions of asymptotically optimal codebooks according to the Welch bound ⋮ A further construction of asymptotically optimal codebooks with multiplicative characters ⋮ Codebooks from generalized bent \(\mathbb{Z}_4\)-valued quadratic forms ⋮ Nearly optimal codebooks based on generalized Jacobi sums ⋮ New Constructions of Codebooks Nearly Meeting the Welch Bound
Cites Work
- Codes with the same weight distributions as the Goethals codes and the Delsarte-Goethals codes
- 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
- Grassmannian frames with applications to coding and communication
- 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
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Optimal codebooks achieving the Levenshtein bound from generalized bent functions over \(\mathbb {Z}_{4}\)
