How to Detect and Construct N-matrices

New Extremal Binary Self-Dual Codes from Block Circulant Matrices and Block Quadratic Residue Circulant Matrices

In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual codes of various lengths over F2 and F2 + uF2. Using extensions, neighbours and sequences of neighbours, we construct many new self-dual codes. In particular, we construct one new self-dual code of length 66 and 51 new self-dual codes of length 68.

New Self-Dual Codes from 2x2 Block Circulant Matrices, Group Rings and Neighbours of Neighbours

In this paper, we construct self-dual codes from a construction that involves 2x2 block circulant matrices, group rings and a reverse circulant matrix. We provide conditions whereby this construction can yield self-dual codes. We construct self-dual codes of various lengths over F2, F2 + uF2 and F4 + uF4. Using extensions, neighbours and neighbours of neighbours, we construct 32 new self-dual codes of length 68.

On Construction of weighted orthogonal matrices over finite field and its application in cryptography

In this article, we propose a method to construct self orthogonal matrix, orthogonal matrix and anti orthogonal matrix over the finite field. Orthogonal matrices has numerous applications in cryptography, so here we demonstrate the application of weighted orthogonal matrix into cryptography. Using the proposed method of construction we see that it is very easy to transmit the private key and can easily convert the encrypted message into original message and at the same time it will be difficult to get the key matrix for intruder.

关于幂等矩阵的一个注记：偏序结构与构造

A Note on Idempotent Matrices: The Poset Structure and The Construction

本文从偏序结构与构造两方面研究除环及主理想整环上的幂等矩阵，利用块分解刻画偏序，借助Smith标准形给出等价条件，并推广至唯一分解整环及Kronecker积等构造。

Set-theoretic solutions of the Yang-Baxter equation and new classes of R-matrices

We describe several methods of constructing R-matrices that are dependent upon many parameters, for example unitary R-matrices and R-matrices whose entries are functions. As an application, we construct examples of R-matrices with prescribed singular values. We characterise some classes of indecomposable set-theoretic solutions of the quantum Yang-Baxter equation (QYBE) and construct R-matrices related to such solutions. In particular, we establish a correspondence between one-generator braces and indecomposable, non-degenerate involutive set-theoretic solutions of the QYBE, showing that such …

Derivatives of triangular, Toeplitz, circulant matrices and matrices of other forms over semirings

In this article we construct examples of derivations in matrix semirings. We study hereditary and inner derivations, derivatives of diagonal, triangular, Toeplitz, circulant matrices and of matrices of other forms and prove theorems for derivatives of matrices of these forms.