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Optimal ternary linear codes. (English) Zbl 0756.94008
Summary: Let n q (k,d) denote the smallest value of n for which there exists a linear [n,k,d]-code over GF(q). An [n,k,d]-code whose length is equal to n q (k,d) is called optimal. The problem of finding n q (k,d) has received much attention for the case q=2. We generalize several results to the case of an arbitrary prime power q as well as introducing new results and a detailed methodology to enable the problem to be tackled over any finite field. In particular, we study the problem with q=3 and determine n 3 (k,d) for all d when k4, and n 3 (5,d) for all but 30 values of d.

94B05General theory of linear codes
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