Improving the Upper Bounds on the Covering Radii of Binary Reed–Muller Codes
From MaRDI portal
Publication:3548051
DOI10.1109/TIT.2006.887494zbMath1192.94139MaRDI QIDQ3548051
Publication date: 21 December 2008
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
Bounds on codes (94B65) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory (94B75)
Related Items (22)
On third-order nonlinearity of biquadratic monomial Boolean functions ⋮ MORE VECTORIAL BOOLEAN FUNCTIONS WITH UNBOUNDED NONLINEARITY PROFILE ⋮ On the global avalanche characteristics between two Boolean functions and the higher order nonlinearity ⋮ On the lower bounds of the second order nonlinearities of some Boolean functions ⋮ Third-order nonlinearities of a subclass of Kasami functions ⋮ On the second-order nonlinearity of the hidden weighted bit function ⋮ On higher order nonlinearities of Boolean functions ⋮ On the covering radius of the third order Reed-Muller code \(\mathrm{RM}(3, 7)\) ⋮ The lower bound on the second-order nonlinearity of a class of Boolean functions with high nonlinearity ⋮ On the number of the rational zeros of linearized polynomials and the second-order nonlinearity of cubic Boolean functions ⋮ Unnamed Item ⋮ New bounds on the covering radius of the second order Reed-Muller code of length 128 ⋮ Higher-order nonlinearity of Kasami functions ⋮ On the nonlinearity of Boolean functions with restricted input ⋮ A trigonometric sum sharp estimate and new bounds on the nonlinearity of some cryptographic Boolean functions ⋮ A comparison of Carlet's second-order nonlinearity bounds ⋮ On the Higher Order Nonlinearities of Boolean Functions and S-Boxes, and Their Generalizations ⋮ Efficient Computation of the Best Quadratic Approximations of Cubic Boolean Functions ⋮ The lower bounds on the second order nonlinearity of three classes of Boolean functions with high nonlinearity ⋮ An improved list decoding algorithm for the second order Reed-Muller codes and its applications ⋮ The covering radius of the Reed-Muller code \(\text{RM}(2, 7)\) is \(40\) ⋮ On the higher-order nonlinearity of a Boolean bent function class (constructed via Niho power functions)
This page was built for publication: Improving the Upper Bounds on the Covering Radii of Binary Reed–Muller Codes
