Some new bounds on LCD codes over finite fields

TL;DR

This paper investigates bounds and properties of LCD codes over finite fields, providing enumeration results, exact values, and demonstrating differences from linear codes over small fields.

Contribution

It establishes that LCD codes are not equivalent to linear codes over small finite fields and computes specific bounds and exact values for certain parameters.

Findings

Binary optimal LCD codes are enumerated.

Exact value of LD(n,2) over  and  is determined.

Bounds for LCD codes over are studied.

Abstract

In this paper, we show that LCD codes are not equivalent to linear codes over small finite fields. The enumeration of binary optimal LCD codes is obtained. We also get the exact value of LD$(n,2)$ over $\mathbb{F}_3$ and $\mathbb{F}_4$. We study the bound of LCD codes over $\mathbb{F}_q$.