On the normality of multiple covering codes

AbstractA binary code C of length n is called a μ-fold r-covering if every binary word of length n is within Hamming distance r of at least μ codewords of C. The normality and the amalgamated direct sum (ADS) construction of 1-fold coverings have been extensively studied. In this paper we generalize the concepts of subnormality and normality to μ-fold coverings and discuss how the ADS construction can be applied to them. In particular, we show that for r = 1, 2 all binary linear μ-fold r-coverings of length at least 2r + 1 and μ-fold normal