Quantum-dot Cellular Automata (QCA) is a prominent paradigm that is considered to continue its dominance in thecomputation at deep sub-micron regime in nanotechnology. The QCA realizations of five-input Majority Voter based multilevel parity generator circuits have been introduced in recent years. However, no attention has been paid towards the QCA instantiation of the generic (n-bit) even and ...

Quantum-dot Cellular Automata (QCA) is a prominent paradigm that is considered to continue its dominance in thecomputation at deep sub-micron regime in nanotechnology. The QCA realizations of five-input Majority Voter based multilevel parity generator circuits have been introduced in recent years. However, no attention has been paid towards the QCA instantiation of the generic (n-bit) even and ...

In traditional parity space approaches, a parity vector with a low order means a simple online realization but a bad performance, while that with a high order leads to a good performance but an unacceptable calculation amount. In this paper, by introducing a simple scalar IIR (Infinite Impulse Response) filter, a new kind of parity relation based residual generator and the corresponding optimiz...

In this letter, we propose an appealing class of nonbinary quasi-cyclic low-density parity-check (QC-LDPC) cycle codes. The parity-check matrix is carefully designed such that the corresponding generator matrix has some nice properties: 1) systematic, 2) quasi-cyclic, and 3) sparse, which allows a parallel encoding with low complexity. Simulation results show that the performance of the propose...

This paper studies the fault detection problem of linear periodic systems. The aim is to design residual generators, which deliver a residual signal fully decoupled from unknown disturbances. First, a periodic parity relation based full decoupling residual generator with a periodic varying parity vector is designed. Then, a periodic observer based full decoupling residual generator is obtained....

Let q denote the finite field GF (q) and let b be a positive integer. MDS codes over the symbol alphabet b q are considered that are linear over q and have sparse (“low-density”) parity-check and generator matrices over q that are systematic over bq . Lower bounds are presented on the number of nonzero elements in any systematic parity-check or generator matrix of an q-linear MDS code over bq, ...

in this paper, we consider a class of column-weight two quasi-cyclic low-density paritycheck codes in which the girth can be large enough, as an arbitrary multiple of 8. then we devote a convolutional form to these codes, such that their generator matrix can be obtained by elementary row and column operations on the parity-check matrix. finally, we show that the free distance of the convolution...

In transmission and data storage of information security becomes more important in the fast evolution of data exchange. It is more important to protect the confidential data from unauthorized access. To overcome that difficulty, we examine the Advanced Encryption Standard (AES) and modify it, to reduce the calculation of algorithm and for improving the data transmission. In modified AES algorit...

We present an efficient new method of obtaining a generator matrix G from certain types of parity check matrices with a defective cyclic block structure. This novel approach describes parity check and generator matrices in terms of polynomials. Moreover, by using this polynomial algebra we have found efficient ways to implement the scheme. In addition, this method is as such interesting as it a...

In this paper we study Z2Z4Z8-additive codes, which are the extension of recently introduced Z2Z4-additive codes. We determine the standard forms of the generator and parity-check matrices of Z2Z4Z8-additive codes. Moreover, we investigate Z2Z4Z8-cyclic codes giving their generator polynomials and spanning sets. We also give some illustrative examples of both Z2Z4Z8-additive codes and Z2Z4Z8-cy...