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On the minimum length of linear codes over \(\mathbb{F}_5\). (English) Zbl 1406.94088
Summary: We construct a lot of new \([n, 5, d]_5\) codes close to the Griesmer bound and prove the nonexistence of some Griesmer codes to determine the exact value of \(n_5(5, d)\) or to improve the known upper bound on \(n_5(5, d)\), where \(n_q(k, d)\) is the minimum length \(n\) for which an \([n, k, d]_q\) code exists. We also give the updated table for \(n_5(5, d)\) for all \(d\) except some known cases.

MSC:
94B05 Linear codes, general
94B65 Bounds on codes
Software:
Q-extension
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References:
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