We consider generalized Preparata codes with a noncommutative group operation. These codes are shown to induce new partitions of Hamming codes into cosets of these Preparata codes. The constructed partitions induce 2-resolvable Steiner quadruple systems S(n, 4, 3) (i.e., systems S(n, 4, 3) that can be partitioned into disjoint Steiner systems S(n, 4, 2)). The obtained partitions of systems S(n, 4, 3) into systems S(n, 4, 2) are not equivalent to such partitions previously known.
Problems of Information Transmission – Springer Journals
Published: Jul 13, 2016
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