# The parameters of a family of linear codes

## TL;DR

This paper constructs a broad family of linear codes from almost bent and perfect nonlinear functions, determining their parameters and demonstrating their optimality for applications in secret sharing and combinational designs.

## Contribution

It introduces new linear codes derived from special functions, with explicit parameters and optimality proofs, expanding coding theory applications.

## Key findings

- Constructed linear codes from almost bent and perfect nonlinear functions.
- Determined parameters and proved optimality of some codes.
- Applied codes to secret sharing schemes and combinational designs.

## Abstract

A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the sense that they meet certain bounds on linear codes. Applications of these codes in secret sharing schemes and combinational designs are presented.