The weight hierarchies of outer product codes (Q1586768)

The concepts of generalized Hamming weight and weight hierarchy of linear codes were introduced by \textit{V. K. Wei} [IEEE Trans. Inf. Theory 37, 1412-1418 (1991; Zbl 0735.94008)] and motivated by cryptographical applications. The method of combining two codes, called outer product, was presented by \textit{R. Brualdi, N. Cai}, and \textit{V. Pless} [Discrete Math. 102, 239-247 (1992; Zbl 0751.94008)]. The author studies weight hierarchies of outer product codes. In particular, the situation when one or both of the codes are self-complementary is considered. The results are used to compute weight hierarchies of Reed-Muller codes.