Correction to "On normal and subnormal q-ary codes"

No abstrac

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

Covering Radius 1985-1994

We survey important developments in the theory of covering radius during the period 1985-1994. We present lower bounds, constructions and upper bounds, the linear and nonlinear cases, density and asymptotic results, normality, specific classes of codes, covering radius and dual distance, tables, and open problems

On normal and subnormal q-ary codes

The authors extend to the q-ary case the notions of a normal code, a subnormal code, and the amalgamated direct sum construction, in order to investigate problems related to the covering radius of codes. For example, the authors prove that every nonbinary nontrivial perfect code is absubnormal. They also include some linear-programming lower bounds on ternary codes with covering radius 2 or 3