Asymptotic bounds on the covering radius of binary codes

Asymptotic covering properties of families of binary codes are studied. A Gaussian approximation to the weight distribution of translates for codes of high strength is used. From this an upper bound on the covering radius of these codes is deduced. Applications include Reed-Muller codes, quadratic residue codes, and BCH codes. Sufficient conditions for a family of codes to have best possible covering radius (asymptotically perfect codes) are derived.<
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