Some new bounds on LCD codes over finite fields

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 ${\mathbb{F}}_q$.

References in corpus (8)

• LCD codes over ${\mathbb{F}}_q$ are as good as linear codes for q at least four
• Binary linear complementary dual codes
• The reversible negacyclic codes over finite fields
• Matrix-Product Complementary dual Codes
• Linear codes over Fq which are equivalent to LCD codes
• On MDS Negacyclic LCD Codes
• New characterization and parametrization of LCD Codes
• Constructions of optimal LCD codes over large finite fields

Cited by in corpus (2)

• Characterization and classification of optimal LCD codes
• Binary LCD Codes from ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$