A method to generate a large number of M-ary Perfect Periodic Autocorrelation (PPAC) codes of length N, with good correlation properties, is presented. N+1 perfect sequences are obtained if an inverse discrete Fourier transform (IDFT) is applied to a specific subset of N+1 bipolar sequences derived from maximal-length sequences. This set of perfect sequences has a maximum absolute value of peri...

The k-ary n-cube is one of the most popular interconnection networks for parallel computing. This paper addresses the size of a largest connected component of a faulty k-ary n-cube. We prove that, in a k-ary n-cube (k ≥ 4 and n ≥ 2) with up to 4n – 2 faulty vertices, all fault-free vertices but at most two constitute a connected component. Moreover, this assertion holds if and only if the set o...

Breast cancer is currently one of the leading causes of death among women worldwide. This paper presents an approach for detecting in digital mammograms not only the detection and early stage of tumors can also detectable. In difficulty of image segmentation found misclassified pixels leads to ambiguity at correct detection of boundary. The effective classification is possible by NN Classifier....

‎Suppose $n$ is a fixed positive integer‎. ‎We introduce the relative n-th non-commuting graph $Gamma^{n} _{H,G}$‎, ‎associated to the non-abelian subgroup $H$ of group $G$‎. ‎The vertex set is $Gsetminus C^n_{H,G}$ in which $C^n_{H,G} = {xin G‎ : ‎[x,y^{n}]=1 mbox{~and~} [x^{n},y]=1mbox{~for~all~} yin H}$‎. ‎Moreover‎, ‎${x,y}$ is an edge if $x$ or $y$ belong to $H$ and $xy^{n}eq y^{n}x$ or $x...

This paper studies coding schemes for the q-ary symmetric channel based on binary low-density parity-check (LDPC) codes that work for any alphabet size q = 2, m ∈ N, thus complementing some recently proposed packet-based schemes requiring large q. First, theoretical optimality of a simple layered scheme is shown, then a practical coding scheme based on a simple modification of standard binary L...

The paper deals with the perfect 1-error correcting codes over a finite field with q elements (briefly q-ary 1-perfect codes). We show that the orthogonal code to the q-ary non-full-rank 1-perfect code of length n = (q − 1)/(q − 1) is a q-ary constant-weight code with Hamming weight equals to qm−1 where m is any natural number not less than two. We derive necessary and sufficient conditions for...

We provide a complete classification of the n-ary semigroup structures defined by polynomial functions over infinite commutative integral domains with identity, thus generalizing G lazek and Gleichgewicht’s classification of ternary semigroups.