Let $X$ be a $BCH$-algebra and $I$ be an ideal of $X$. In this paper, we introduce the concept of $sqrt{I}$. We show that it is an ideal of $X$, when $I$ is closed ideal of $X$. Then we verify some useful properties of it. We prove that it is the ::::union:::: of all $k-$nil ideals of $I$. Moreover, if $I$ is a closed ideal of $X$, then $sqrt{I}$ is a closed translation ideal and so we can cons...

Absolute coset leaders were first proposed by the authors which have advantages in constructing binary LCD BCH codes. As a continue work, this paper we focus on ternary linear Firstly, find largest, second and third largest absolute of primitive Secondly, present three classes codes determine their weight distributions. Finally, obtain some calculate However, calculation distributions two these...

The purpose of this paper is to study the Bose, Chaudhuri, and Hocquenghem (BCH) code, with an aim to simulate the encoding and decoding processes. The gain of the proposed code in investigated through applying it to binary phase sift keying (BPSK) modulation scheme in symmetric additive white Gaussian noise (AWGN) channel. The bit error probability (BEP) of coded (63, 36) BCH system was evalua...

In this letter, we propose a simplified step-by-step decoding algorithm for t-error-correcting binary Bose-ChaudhuriHocquenghem (BCH) codes based on logical analysis. Compared to the conventional stepby-step decoding algorithm, the computation complexity of this decoder is much less, since it significantly reduces the matrix calculation and the operations of multiplication. key words: BCH code,...

BCH decoding usually involves the evaluation of the error-locator polynomial. This is often achieved with the Berlekamp-Massey algorithm, which requires about O(t) computational steps, where t is the error-correction capability of the BCH code. The evaluation of the errorlocator polynomial may also be computed using fast inversion techniques for Hankel matrices. It will be shown that only O(lt)...

Recommendations from the Pediatric Endocrine Society for Evaluation and Management of Persistent Hypoglycemia in Neonates, Infants, and Children Paul S. Thornton, MB, BCh, Charles A. Stanley, MD, Diva D. De Leon, MD, MSCE, Deborah Harris, PhD, Morey W. Haymond, MD, Khalid Hussain, MD, MPH, Lynne L. Levitsky, MD, Mohammad H. Murad, MD, MPH, Paul J. Rozance, MD, Rebecca A. Simmons, MD, Mark A. Sp...

Discovered by Bose, Chaudhuri and Hocquenghem [1], [4], the BCH family of error correcting codes are one of the most studied families in coding theory. They are also among the best performing codes, particularly when the number of errors being corrected is small relative to the code length. In this article we consider binary codes with minimum distance of 7. We construct new families of codes w...

In this paper we study a class of graph codes with BCH component codes as affine variety codes. We are able to find some optimal binary and ternary codes as Tanner codes with BCH component codes. We choose a special subgraph of the point-line incidence plane of P(2, q) as the Tanner graph, and we are able to describe the codes using Gröbner basis.

An interesting class of l inear error-correcting codes has been found by Goppa [3], [4]. This paper presents algebraic decoding algorithms for the Goppa codes. These algorithms are only a little more complex than Berlekamp’s well-known algorithm for BCH codes and, in fact, make essential use of his procedure. Hence the cost of decoding a Goppa code is similar to the cost of decoding a BCH code ...