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Some new lower bounds for ternary covering codes. (English) Zbl 0917.94021

Electron. J. Comb. 3, No. 2, Research paper R23, 14 p. (1996); printed version J. Comb. 3, No. 2, 527-540 (1996).
Summary: In a previous paper [L. Habsieger, Discrete Math. 176, 115-130 (1997; Zbl 0898.94016)] the author studied binary codes with covering radius one via their characteristic functions. This gave him an easy way of obtaining congruence properties and of deriving interesting linear inequalities. In this paper he extends this approach to ternary covering codes. He improves on lower bounds for ternary 1-covering codes, the so-called football pool problem, when 3 does not divide \(n-1\). He also give new lower bounds for some covering codes with a covering radius greater than one.

MSC:

94B75 Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory
94B65 Bounds on codes

Citations:

Zbl 0898.94016
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