The Minimum Distance of Some Narrow-Sense Primitive BCH Codes

The Minimum Distance of Some Narrow-Sense Primitive BCH Codes

Due to wide applications of BCH codes, the determination of their minimum distance is of great interest. However, this is a very challenging problem for which few theoretical results have been reported in the last four decades. Even for the narrow-sense primitive BCH codes, which form the most well-studied subclass of BCH codes, there are very few theoretical results on the minimum distance. In...

The dimension and minimum distance of two classes of primitive BCH codes

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, ...

On the Dimension, Minimum Distance, and Duals of Primitive BCH Codes

We determine the dimension and in some cases the minimum distance of primitive, narrow sense BCH codes of length n with small designed distance. We show that such a code contains its Euclidean dual code and, when the size of the field is a perfect square, also its Hermitian dual code. We establish two series of quantum error-correcting codes.

The True Minimum Distance of Some Narrow - SenseBCH - Codes of Length 255 Georg

Cyclic and BCH codes whose minimum distance equals their maximum BCH bound

In this paper we study the family of cyclic codes such that its minimum distance reaches the maximum of its BCH bounds. We also show a way to construct cyclic codes with that property by means of computations of some divisors of a polynomial of the form xn − 1. We apply our results to the study of those BCH codes C, with designed distance δ, that have minimum distance d(C) = δ. Finally, we pres...