Weight Distribution of a Class of Cyclic Codes with Arbitrary Number of Zeros

TL;DR

This paper investigates a broad class of cyclic codes with any number of zeros, providing a comprehensive determination of their weight distributions, which is a challenging problem in coding theory.

Contribution

The paper introduces a new class of cyclic codes with arbitrary zeros and explicitly determines their weight distributions, advancing understanding in coding theory.

Findings

Explicit weight distributions for the new class of cyclic codes

Applicable to codes with any number of zeros

Enhances decoding efficiency in digital communication

Abstract

Cyclic codes have been widely used in digital communication systems and consume electronics as they have efficient encoding and decoding algorithms. The weight distribution of cyclic codes has been an important topic of study for many years. It is in general hard to determine the weight distribution of linear codes. In this paper, a class of cyclic codes with any number of zeros are described and their weight distributions are determined.