Two-Weight and a Few Weights Trace Codes over ${\mathbb{F}}_q+u{\mathbb{F}}_q$

Abstract

Let $p$ be a prime number, $q=p^s$ for a positive integer $s$. For any positive divisor $e$ of $q-1$, we construct an infinite family codes of size $q^{2m}$ with few Lee-weight. These codes are defined as trace codes over the ring $R={\mathbb{F}}_q+u{\mathbb{F}}_q$, $u^2=0$. Using Gauss sums, their Lee weight distributions are provided. When $\gcd (e,m)=1$, we obtain an infinite family of two-weight codes over the finite field ${\mathbb{F}}_q$ which meet the Griesmer bound. Moreover, when $\gcd (e,m)=2,3$ or $4$ we construct new infinite family codes with at most five-weight.

References in corpus (1)

• New Classes of $p$-ary Few Weights Codes

Cited by in corpus (1)

• A class of linear codes with few weights