# On cyclic codes of composite length and the minimal distance

## TL;DR

This paper develops a general method for analyzing cyclic codes of composite length, explains the optimality of certain codes, and introduces new constructions that yield many best codes and applications to convolutional codes.

## Contribution

It introduces a new general method for cyclic codes of composite length and provides a novel construction producing many optimal codes.

## Key findings

- Many constructed codes are best cyclic codes for given parameters.
- The new method helps estimate minimal distances of cyclic codes.
- Constructed codes can be used to build convolutional codes with large free distance.

## Abstract

In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and dimension over the same finite field. However, not much is known about these codes. In this paper we explain some of the mysteries of the numerical data by developing a general method on cyclic codes of composite length and on estimating the minimal distance. Inspired by the new method, we also provide a general construction of cyclic codes of composite length. Numerical data shows that it produces many best cyclic codes as well. Finally, we point out how these cyclic codes can be used to construct convolutional codes with large free distance.