FEW-WEIGHT CODES FROM TRACE CODES OVER Rk

We construct two families of few-weight codes for the Lee weight over the ring Rk based on two di ff erent 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.