A class of few-Lee weight ℤ_2[u]-linear codes using simplicial complexes and minimal codes via Gray map
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Recently some mixed alphabet rings are involved in constructing few-Lee weight additive codes with optimal or minimal Gray images using suitable defining sets or down-sets. Inspired by these works, we choose the mixed alphabet ring ℤ_2ℤ_2[u] to construct a special class of linear code C_L over ℤ_2[u] with u^2=0 by employing simplicial complexes generated by a single maximal element. We show that C_L has few-Lee weights by determining the Lee weight distribution of C_L. Theoretically, this shows that we may employ simplicial complexes to obatin few-weight codes even in the case of mixed alphabet rings. We show that the Gray image of C_L is self-orthogonal and we have an infinite family of minimal codes over ℤ_2 via Gray map, which can be used to secret sharing schemes.
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