The Walsh transform of a class of monomial functions and cyclic codes

DOI10.1007/S12095-014-0109-2zbMath1365.94673OpenAlexW1994940311MaRDI QIDQ892299

Qin Yue, Chengju Li

Publication date: 18 November 2015

Published in: Cryptography and Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12095-014-0109-2

zbMATH Keywords

value distributionGauss sumsGauss periodscyclic codeWalsh transform

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Other character sums and Gauss sums (11T24) Cyclic codes (94B15)

Related Items (6)

A construction of binary linear codes from Boolean functions ⋮ Two classes of two-weight linear codes ⋮ A class of functions with low-valued Walsh spectrum ⋮ Several classes of exponential sums and three-valued Walsh spectrums over finite fields ⋮ Binary and ternary sequences with a few cross correlations ⋮ The values of two classes of Gaussian periods in index 2 case and weight distributions of linear codes

Cites Work

• Unnamed Item
• Unnamed Item
• The weight distribution of a class of \(p\)-ary cyclic codes
• Crosscorrelation of \(m\)-sequences, exponential sums, bent functions and Jacobsthal sums
• Monomial bent functions and Stickelberger's theorem
• New pairs of \(m\)-sequences with 4-level cross-correlation.
• Some results about the cross-correlation function between two maximal linear sequences
• Hamming weights in irreducible cyclic codes
• Explicit evaluation of certain exponential sums of binary quadratic functions
• \(p\)-ary and \(q\)-ary versions of certain results about bent functions and resilient functions
• Several New Classes of Bent Functions From Dillon Exponents
• A Class of Binomial Bent Functions Over the Finite Fields of Odd Characteristic
• Monomial and quadratic bent functions over the finite fields of odd characteristic
• Monomial bent functions
• Cross correlation of m-sequences of different lengths
• On the correlation distribution of the Coulter-Matthews decimation
• The weight distribution of a class of linear codes from perfect nonlinear functions
• A New Three-Valued Cross Correlation Between$m$-Sequences of Different Lengths
• Characterization of $m$-Sequences of Lengths $2^{2k}-1$ and $2^{k}-1$ With Three-Valued Cross Correlation
• Value Distributions of Exponential Sums From Perfect Nonlinear Functions and Their Applications
• Generalized Kasami Sequences: The Large Set
• A New Family of Four-Valued Cross Correlation Between $m$-Sequences of Different Lengths
• On the Weight Distributions of Two Classes of Cyclic Codes
• Cyclic Codes and Sequences From Generalized Coulter–Matthews Function
• On subfield subcodes of modified Reed-Solomon codes (Corresp.)
• Period polynomials and Gauss sums for finite fields
• Binary m-sequences with three-valued crosscorrelation: a proof of Welch's conjecture
• Ternary m-sequences with three-valued cross-correlation function: new decimations of Welch and Niho type
• Period-Different $m$-Sequences With at Most Four-Valued Cross Correlation
• Cyclic Codes and Sequences: The Generalized Kasami Case
• On the Walsh Transform of a Class of Functions From Niho Exponents

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