It is impossible to introduce combinatorial designs and linear codes without basic tools in
certain mathematical areas. In this chapter, we give a brief introduction to cyclotomy, finite …

Most coding theory experts date the origin of the subject with the 1948 publication of A
Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has …

BCH codes are a subclass of cyclic codes with many interesting properties. In many cases
BCH codes are the best linear codes. For example, among all binary cyclic codes of odd …

It is well-known that cyclic codes have efficient encoding and decoding algorithms. In recent
years, antiprimitive BCH codes have attracted a lot of attention. The objective of this paper is …

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 …

The self-orthogonality and divisibility are two important properties of linear codes. It is
interesting to establish relationship between them. By the well-known Gleason-Pierce-Ward …

In this paper, we study LCD BCH codes over the finite field GF (q) with two types of lengths
n, where n= ql+ 1 and n=(ql+ 1)/(q+ 1). Several classes of LCD BCH codes are given and …

As a special subclass of cyclic codes, BCH codes have wide applications in communication
and storage systems. A BCH code of length over is always relative to an-th primitive root of …

Binary cyclic codes with parameters are very interesting, as their minimum distances have a
square-root bound. The binary quadratic residue codes and the punctured binary Reed …

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 …