Construction of cyclotomic codebooks nearly meeting the Welch bound

DOI10.1007/S10623-011-9549-2zbMath1236.94014OpenAlexW2020089954MaRDI QIDQ766244

Aixian Zhang, Ke Qin Feng

Publication date: 23 March 2012

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-011-9549-2

zbMATH Keywords

codebookGauss sumdifference setGauss periodWelch boundcyclotomic numberalmost difference setcyclotomic class

Mathematics Subject Classification ID

Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Communication theory (94A05)

Related Items (18)

Nearly optimal codebooks from generalized Boolean bent functions over \(\mathbb{Z}_4\) ⋮ Six constructions of asymptotically optimal codebooks via the character sums ⋮ Hybrid character sums and near-optimal partial Hadamard codebooks ⋮ Character sums over a non-chain ring and their applications ⋮ Gaussian sums, hyper Eisenstein sums and Jacobi sums over a local ring and their applications ⋮ Cayley sum graphs and their applications to codebooks ⋮ A new class of near-optimal partial Fourier codebooks from an almost difference set ⋮ Optimal codebooks achieving the Levenshtein bound from generalized bent functions over \(\mathbb {Z}_{4}\) ⋮ More constructions of near optimal codebooks associated with binary sequences ⋮ Unit time-phase signal sets with the explicit maximum cross ambiguity amplitudes ⋮ Two constructions of asymptotically optimal codebooks according to the Welch bound ⋮ Two classes of near-optimal codebooks with respect to the Welch bound ⋮ Codebooks from generalized bent \(\mathbb{Z}_4\)-valued quadratic forms ⋮ Two constructions of asymptotically optimal codebooks via the trace functions ⋮ New constructions of asymptotically optimal codebooks via cyclotomic classes of order 8 ⋮ Two constructions of asymptotically optimal codebooks ⋮ Two families of nearly optimal codebooks ⋮ New Constructions of Codebooks Nearly Meeting the Welch Bound

Cites Work

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• A new family of almost difference sets and some necessary conditions
• 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.)
• Almost difference sets and their sequences with optimal autocorrelation

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