The combinatorics of LCD codes: linear programming bound and orthogonal matrices
Linear complementary dual (LCD) codes are binary linear codes that meet their dual trivially.
We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs …
We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs …
[HTML][HTML] Constructions of optimal LCD codes over large finite fields
In this paper 1, we prove existence of optimal complementary dual codes (LCD codes) over
large finite fields. We also give methods to generate orthogonal matrices over finite fields …
large finite fields. We also give methods to generate orthogonal matrices over finite fields …
[HTML][HTML] Self-dual codes and orthogonal matrices over large finite fields
In this paper, we give algorithms and methods of construction of self-dual codes over finite
fields using orthogonal matrices. Randomization in the orthogonal group, code extension …
fields using orthogonal matrices. Randomization in the orthogonal group, code extension …
Self-dual bent functions
A bent function is called self-dual if it is equal to its dual. It is called anti-self-dual if it is equal
to the complement of its dual. A spectral characterisation in terms of the Rayleigh quotient of …
to the complement of its dual. A spectral characterisation in terms of the Rayleigh quotient of …
[HTML][HTML] Metrical properties of self-dual bent functions
A Kutsenko - Designs, Codes and Cryptography, 2020 - Springer
In this paper we study metrical properties of Boolean bent functions which coincide with their
dual bent functions. We propose an iterative construction of self-dual bent functions in n+ 2 …
dual bent functions. We propose an iterative construction of self-dual bent functions in n+ 2 …
Classification of self dual quadratic bent functions
XD Hou - Designs, Codes and Cryptography, 2012 - Springer
We classify all self dual and anti self dual quadratic bent functions in 2 n variables under the
action of the orthogonal group O (2n,\mathbb F_2). This is done through a classification of all …
action of the orthogonal group O (2n,\mathbb F_2). This is done through a classification of all …
Towards the classification of self-dual bent functions in eight variables
T Feulner, L Sok, P Solé, A Wassermann - Designs, codes and …, 2013 - Springer
In this paper, we classify quadratic and cubic self-dual bent functions in eight variables with
the help of computers. There are exactly four and 45 non-equivalent self-dual bent functions …
the help of computers. There are exactly four and 45 non-equivalent self-dual bent functions …
New constructions of optimal binary LCD codes
G Wang, S Liu, H Liu - Finite Fields and Their Applications, 2024 - Elsevier
Linear complementary dual (LCD) codes provide an optimum linear coding solution for the
two-user binary adder channel. LCD codes also can be used against side-channel attacks …
two-user binary adder channel. LCD codes also can be used against side-channel attacks …
Self-dual Hadamard bent sequences
A new notion of bent sequence related to Hadamard matrices was introduced recently,
motivated by a security application (Solé, et al., 2021). The authors study the self-dual class …
motivated by a security application (Solé, et al., 2021). The authors study the self-dual class …