New pairs of \(m\)-sequences with 4-level cross-correlation.

DOI10.1016/j.ffa.2004.09.001zbMath1190.11011OpenAlexW2108420898MaRDI QIDQ955198

Petri Rosendahl, Tor Helleseth

Publication date: 19 November 2008

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2004.09.001

zbMATH Keywords

Cross-correlationFinite fieldsBinary \(m\)-sequences

Mathematics Subject Classification ID

Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30) Sequences (mod (m)) (11B50)

Related Items (13)

Several new classes of (balanced) Boolean functions with few Walsh transform values ⋮ A construction of binary linear codes from Boolean functions ⋮ A survey on the applications of Niho exponents ⋮ A class of functions with low-valued Walsh spectrum ⋮ Two-valued cross correlation distributions between binary \(m\) sequences and their decimation sequences ⋮ The Walsh transform of a class of monomial functions and cyclic codes ⋮ Several classes of Niho type Boolean functions with few Walsh transform values ⋮ Several Classes of Boolean Functions with Four-Valued Walsh Spectra ⋮ Boolean functions with four-valued Walsh spectra ⋮ Crosscorrelation of \(m\)-sequences, exponential sums, bent functions and Jacobsthal sums ⋮ On Niho type cross-correlation functions of \(m\)-sequences ⋮ Two families of Niho sequences having four-valued cross correlation with \(m\)-sequences ⋮ A generalization of Niho's theorem

Cites Work

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• Some results about the cross-correlation function between two maximal linear sequences
• One-to-one highly nonlinear power functions on \(\mathrm{GF}(2^n)\)
• Binary m-sequences with three-valued crosscorrelation: a proof of Welch's conjecture
• On the odd and the aperiodic correlation properties of the Kasami sequences
• Some new three-valued crosscorrelation functions for binary m-sequences
• The weight enumerators for several classes of subcodes of the 2nd order binary Reed-Muller codes
• Maximal recursive sequences with 3-valued recursive cross-correlation functions (Corresp.)
• A proof of the Welch and Niho conjectures on cross-correlations of binary \(m\)-sequences

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