FEW-WEIGHT CODES FROM TRACE CODES OVER

Abstract

We construct two families of few-weight codes for the Lee weight over the ring $R_{k}$ based on two different defining sets. For the first defining set, taking the Gray map, we obtain an infinite family of binary two-weight codes which are in fact $2^{k}$-fold replicated MacDonald codes. For the second defining set, we obtain two infinite families of few-weight codes. These few-weight codes can be used to implement secret-sharing schemes.