On the Covering Radius Problem for Codes I . Bounds on Normalized Covering Radius
نویسنده
چکیده
In this two-part paper we introduce the notion of a stable code and give a new upper bound on the normalized covering radius ofa code. The main results are that, for fixed k and large n, the minimal covering radius t[n, k] is realized by a normal code in which all but one of the columns have multiplicity l; hence tin + 2, k] t[n, k] + for sufficiently large n. We also show that codes with n _-< 14, k-< 5 or dmin 5 are normal, and we determine the covering radius of all proper codes of dimension k _-< 5. Examples of abnormal nonlinear codes are given. In Part we investigate the general theory of normalized covering radius, while in Part II [this Journal, 8 (1987), pp. 619-627] we study codes of dimension k-< 5, and normal and abnormal codes.
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