Based on the ideas of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, we present a new method to construct GF(2m ), where m > 0 cyclic low-density paritycheck codes. The construction method produces the dual code idempotent which is used to define the parity-check matrix of the low-density parity-check code. An interesting feature of this construction method is the ability to in...

We consider the Norton algebra associated with a Q -polynomial primitive idempotent of adjacency matrix for distance-regular graph. obtain formula product that we find attractive.

A complex square matrix A is said to be idempotent, or a projector, whenever A2 = A; when A is idempotent, and Hermitian (or real symmetric), it is often called an orthogonal projector, otherwise an oblique projector. Projectors are closely linked to generalized inverses of matrices. For example, for a given matrix A the product PA = AA + is well known as the orthogonal projector on the range (...

The paper was inspired by the question whether it is possible to derive the equality between the rank and trace of an idempotent matrix by using only the idempotency property, without referring to any further features of the matrix. It is shown that such a proof can be obtained by exploiting a general characteristic of the rank of any matrix. An original proof of this characteristic is provided...

Identity transformations, used as skip-connections in residual networks, directly connect convolutional layers close to the input and those close to the output in deep neural networks, improving information flow and thus easing the training. In this paper, we introduce two alternative linear transforms, orthogonal transformation and idempotent transformation. According to the definition and pro...

Multidimensional minimax single facility location problems with Chebyshev distance are examined within the framework of idempotent algebra. A new algebraic solution based on an extremal property of the eigenvalues of irreducible matrices is given. The solution reduces both unconstrained and constrained location problems to evaluation of the eigenvalue and eigenvectors of an appropriate matrix. ...

Abstract In this paper, we exhibit that, in an incline L, the greatest element ‘1’ is the multiplicative identity for the elements of DL, the set of idempotent elements in L. We have discussed the invertibility of matrices over DL and for matrices over an integral incline. We have obtained equivalent conditions for regularity of a matrix over an incline whose idempotent elements are linearly or...

Let Γ denote a bipartite distance-regular graph with diameter D ≥ 4, valency k ≥ 3 and intersection numbers ci , bi (0 ≤ i ≤ D). By a pseudo cosine sequence of Γ we mean a sequence of scalars σ0, . . . , σD such that σ0 = 1 and ciσi−1 + biσi+1 = kσ1σi for 1 ≤ i ≤ D − 1. By an associated pseudo primitive idempotent we mean a nonzero scalar multiple of the matrix ∑D i=0 σi Ai , where A0, . . . , ...

an ideal i of a ring r is called right baer-ideal if there exists an idempotent e 2 r such that r(i) = er. we know that r is quasi-baer if every ideal of r is a right baer-ideal, r is n-generalized right quasi-baer if for each i e r the ideal in is right baer-ideal, and r is right principaly quasi-baer if every principal right ideal of r is a right baer-ideal. therefore the concept of baer idea...