Construction of two-Lee weight codes over

Abstract

This paper is devoted to the construction of two-Lee weight codes over ${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p(v^3=v)$ with type $p^{3k_1}{p}^{2k_2}{p}^{2k_3}{p}^{2k_4}{p}^{k_5}{p}^{k_6}$ based on a distance-preserving Gray map from $({\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p{)}^n$ to ${\mathbb{F}}_p^{3n}$. The necessary conditions for a code over ${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$ to have only two different nonzero weights are given. The existence of two-Lee weight projective codes is also presented. Finally, some examples are also presented to illustrate the algebraic structure of two-Lee weight codes over ${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$.

Keywords:

• gray map
• lee weight
• two-weight codes
• generator matrix
• linear codes

2000 AMS Subject Classifications:

• 94B05
• 94B60

Acknowledgment

This paper is supported by National Natural Science Foundation of China (61202068), Talents youth Fund of Anhui Province Universities (2012SQRL020ZD).