On the normality of multiple covering codes (Q1322275)

A binary code \(C\) of length \(n\) is called a \(\mu\)-fold \(r\)-covering if every binary word of length \(n\) is within Hamming distance \(r\) of at least \(\mu\) codewords of \(C\). The author generalizes the concepts of subnormality and normality to \(\mu\)-fold coverings. He also shows how the ADS (amalgamated direct sum) construction can be applied to them. The author proves that for \(r=1,2\) all binary linear \(\mu\)-fold \(r\)-coverings of length at least \(2r+1\) are \(\mu\)-fold normal.