# Parameters of several families of binary duadic codes and their related codes

## TL;DR

This paper explores various families of binary duadic codes, providing new lower bounds on their minimum distances and analyzing their dual and extended code parameters, advancing understanding of their error-correcting capabilities.

## Contribution

It introduces several new families of binary duadic codes with bounds on minimum distances and investigates their dual and extended code parameters.

## Key findings

- Lower bounds on minimum distances are close to the square-root bound.
- Parameters of dual and extended codes are characterized.
- Partially solves an open problem on minimum distance bounds.

## Abstract

Binary duadic codes are an interesting subclass of cyclic codes since they have large dimensions and their minimum distances may have a square-root bound. In this paper, we present several families of binary duadic codes of length $2^m-1$ and develop some lower bounds on their minimum distances by using the BCH bound on cyclic codes, which partially solves one case of the open problem proposed in \cite{LLD}. It is shown that the lower bounds on their minimum distances are close to the square root bound. Moreover, the parameters of the dual and extended codes of these binary duadic codes are investigated.