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Few-weight codes from trace codes over \(R_k\). (English) Zbl 1430.94097

Summary: 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.

MSC:

94B05 Linear codes (general theory)
94B15 Cyclic codes
94A62 Authentication, digital signatures and secret sharing
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