Codes, graphs, and schemes from nonlinear functions
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Publication:1869033
DOI10.1016/S0195-6698(02)00116-6zbMath1015.05093MaRDI QIDQ1869033
Dmitry G. Fon-Der-Flaass, van Dam, Edwin R.
Publication date: 9 April 2003
Published in: European Journal of Combinatorics (Search for Journal in Brave)
Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Linear codes (general theory) (94B05) Association schemes, strongly regular graphs (05E30) Cryptography (94A60)
Related Items (18)
Crooked maps in \(\mathbb F_{2^n}\) ⋮ The \textit{crooked} property ⋮ On group rings and some of their applications to combinatorics and symmetric cryptography ⋮ Notes on APN functions, semibiplanes and dimensional dual hyperovals ⋮ Componentwise APNness, Walsh uniformity of APN functions, and cyclic-additive difference sets ⋮ The chromatic number and rank of the complements of the Kasami graphs ⋮ A generalization of APN functions for odd characteristic ⋮ The only crooked power functions are \(x^{2^k+2^l}\) ⋮ On APN functions whose graphs are maximal Sidon sets ⋮ On diameter perfect constant-weight ternary codes ⋮ A link between combinatorial designs and three-weight linear codes ⋮ A Partition of the Hypercube into Maximally Nonparallel Hamming Codes ⋮ The combinatorics of Dom de Caen ⋮ Crooked binomials ⋮ On binary Kloosterman sums divisible by 3 ⋮ Unnamed Item ⋮ Improved Bounds on Sizes of Generalized Caps in $AG(n,q)$ ⋮ Quadratic zero-difference balanced functions, APN functions and strongly regular graphs
Cites Work
- Codes, bent functions and permutations suitable for DES-like cryptosystems
- A class of functions and their application in constructing semi-biplanes and association schemes
- Crooked functions, bent functions, and distance regular graphs
- Association schemes related to Kasami codes and Kerdock sets
- Uniformly packed codes and more distance regular graphs from crooked functions
- A sharpening of the Johnson bound for binary linear codes and the nonexistence of linear codes with Preparata parameters
- A family of antipodal distance-regular graphs related to the classical Preparata codes
- Maximally nonlinear functions and bent functions.
- Character sums and difference sets
- Binary m-sequences with three-valued crosscorrelation: a proof of Welch's conjecture
- 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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