Related papers: Some binary BCH codes with length $n=2^m+1$
Bose-Chaudhuri-Hocquenghem (BCH) codes have been intensively investigated. Even so, there is only a little known about primitive BCH codes, let alone non-primitive ones. In this paper, let $q>2$ be a prime power, the dimension of a family…
BCH codes form an important subclass of cyclic codes, and are widely used in compact discs, digital audio tapes and other data storage systems to improve data reliability. As far as we know, there are few results on $q$-ary BCH codes of…
BCH codes and their dual codes are two special subclasses of cyclic codes and are the best linear codes in many cases. A lot of progress on the study of BCH cyclic codes has been made, but little is known about the minimum distances of the…
BCH codes are a significant class of cyclic codes that play an important role in both theoretical research and practical applications. Their strong error-correcting abilities and efficient encoding and decoding methods make BCH codes widely…
BCH and LCD cyclic codes of length $n=\lambda(q^m+1)$ with $\lambda\mid q-1$ are studied. A complete characterization of $q$-cyclotomic cosets modulo $n$ is given: Theorem \ref{th4} provides a necessary and sufficient condition for any…
LCD BCH codes are an important class of cyclic codes which have efficient encoding and decoding algorithms, but their parameters are difficult to determine. The objective of this paper is to study the LCD BCH codes of length…
In this paper, we investigate the first few largest coset leaders modulo $\frac{q^m+1}{\lambda}$ where $\lambda\mid q+1$ and $q$ is an odd prime power, and give the dimensions of some LCD BCH codes of length $\frac{q^m+1}{\lambda}$ with…
BCH codes have been studied for over fifty years and widely employed in consumer devices, communication systems, and data storage systems. However, the dimension of BCH codes is settled only for a very small number of cases. In this paper,…
BCH codes are important error correction codes, widely utilized due to their robust algebraic structure, multi-error correcting capability, and efficient decoding algorithms. Despite their practical importance and extensive study, their…
BCH codes are an important class of linear codes and find extensive utilization in communication and disk storage systems.This paper mainly analyzes the negacyclic BCH code and cyclic BCH code of length $\frac{q^m-1}{2}$. For negacyclic BCH…
BCH codes are an important class of cyclic codes which have applications in satellite communications, DVDs, disk drives, and two-dimensional bar codes. Although BCH codes have been widely studied, their parameters are known for only a few…
BCH codes are an interesting class of cyclic codes due to their efficient encoding and decoding algorithms. In many cases, BCH codes are the best linear codes. However, the dimension and minimum distance of BCH codes have been seldom…
BCH codes with efficient encoding and decoding algorithms have many applications in communications, cryptography and combinatorics design. This paper studies a class of linear codes of length $ \frac{q^m-1}{2}$ over $\mathbb{F}_q$ with…
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…
BCH codes are an interesting class of cyclic codes due to their efficient encoding and decoding algorithms. In the past sixty years, a lot of progress on the study of BCH codes has been made, but little is known about the properties of…
BCH codes form an important class of cyclic codes, which have applications in communication and data storage systems. Although the BCH bound provides a lower bound on the minimum distance of BCH codes, determining the true minimum distances…
Cyclic codes over finite fields are widely employed in communication systems, storage devices and consumer electronics, as they have efficient encoding and decoding algorithms. BCH codes, as a special subclass of cyclic codes, are in most…
Binary cyclic codes have been a hot topic for many years, and significant progress has been made in the study of this types of codes. As is well known, it is hard to construct infinite families of binary cyclic codes [n, n+1/2] with good…
Discovered by Bose, Chaudhuri and Hocquenghem, 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…
Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms as well as their theoretical importance. BCH codes form a subclass of cyclic codes and are very important in both theory and…