Reed-Solomon codes, a type of BCH codes, are widely employed in communication systems, storage devices and consumer electronics. This fact demonstrates the importance of BCH codes – a family of cyclic codes – in practice. In theory, BCH codes are among the best cyclic codes in terms of their error-correcting capability. A subclass of BCH codes are the narrow-sense primitive BCH codes. However, ...

We define the notion of radical in BCH-algebra and investigate the structure of [X; k], a viewpoint of radical in BCH-algebras. 1. Introduction. In 1966, Imai and Iséki [8] and Iséki [9] introduced two classes of abstract algebras: BCK-algebras and BCI-algebras. It is known that the class of BCK-algebras is a proper subclass of the class of BCI-algebras. In 1983, Hu and Li [5, 6] introduced a w...

Modular reduction is the basic building block of many publickey cryptosystems. BCH codes require repeated polynomial reductions modulo the same constant polynomial. This is conceptually very similar to the implementation of public-key cryptography where repeated modular reduction in Zn or Zp are required for some fixed n or p. It is hence natural to try and transfer the modular reduction expert...

VLSI Architectures for Modern Error-Correcting Codes CRC Press Book. Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) codes, and binary. An important class of multipleerror-correcting linear cyclic codes is the class of BCH codes. In fact, BCH code is a generalization of the cyclic Hamming codes. Error correction codes (ECCs) are deployed in digital communication systems to tion 4 recalls...

چکیده: ماتریس­های نمونه­برداری نقش اساسی در حسگری فشرده دارند. این مـاتریس­ها به­صـورت تصـادفی و یقینی قابل ساخت هستند. ماتریس­های یقینی به علت اینکه حافظه کم­تری برای ذخیره­سازی نیاز دارند موردتوجه زیادی قرار گرفته­اند. در این مقاله دسته­ای از ماتریس­های حسگری یقینی، با استفاده از توابع هش ساخته می­شوند. برای این منظور ابتدا یک ماتریس کد اولیه ساخته می­شود، سپس با استفاده از ماتریس توابع هش، ی...

Classical Bose-Chaudhuri-Hocquenghem (BCH) codes C that contain their dual codes can be used to construct quantum stabilizer codes this chapter studies the properties of such codes. It had been shown that a BCH code of length n which contains its dual code satisfies the bound on weight of any non-zero codeword in C and converse is also true. One impressive difficulty in quantum communication an...

The hyperinsulism/hyperammonemia (HI/HA) syndrome is caused by glutamate dehydrogenase (GDH) gain-of-function mutations that reduce the inhibition by GTP, consequently increasing the activity of GDH in vivo. The source of the hyperammonemia in the HI/HA syndrome remains unclear. We examined the effect of systemic activation of GDH on ammonia metabolism in the rat. 2-Aminobicyclo[2,2,1]heptane-2...

This study presents a novel means of shortening a Reed Solomon (RS) code at the bit level, yielding only shortened BCH subcodes. With the use of a certain basis, an RS codes over ) 2 ( m GF is mapped onto a binary image[4], which contains m concatenated BCH sub-codewords and some glue-vector codewords. With the proposed approach, there only exist some shortened BCH subcode generators in the dia...

The CRAL_TRIO protein domain, which is unique to the Sec14 protein superfamily, binds to a diverse set of small lipophilic ligands. Similar domains are found in a range of different proteins including neurofibromatosis type-1, a Ras GTPase-activating Protein (RasGAP) and Rho guanine nucleotide exchange factors (RhoGEFs). Proteins containing this structural protein domain exhibit a low sequence ...